1  50
Next
 First edition  New Jersey : World Scientific Publishing Co. Pte. Ltd. : Higher Education Press, [2023]
 Description
 Book — 1 online resource
 Partielle Differenzialgleichungen. English
 Arendt, Wolfgang, 1950 author.
 Cham, Switzerland : Springer, [2023]
 Description
 Book — xxiv, 452 pages : illustrations ; 25 cm
 Summary

"This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computeraided calculation with Maple™ completes the book. Throughout, three fundamental examples are studied with different tools: Poisson's equation, the heat equation, and the wave equation on Euclidean domains. The BlackScholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upperundergraduate level are assumed."Provided by publisher
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QA374 .A78413 2023  Unknown 
 Cham, Switzerland : Springer, 2023.
 Description
 Book — 1 online resource
 Summary

 Existence and uniqueness of solution for semi linear conservation laws with velocity field in L
 Structural stability of p(x)Laplace problems with Robin type boundary condition
 Weak solutions of antiperiodic discrete nonlinear problems
 Boundary feedback controller over a bluff body for prescribed drag and lift coefficients
 Discrete potential boundary value problems of Kirchhoff type
 From Calculus of Variation to Exterior Differential Calculus: A Presentation and Some New Results
 Existence of local and maximal mild solutions for some nonautonomous functional differential equation with finite delay
 Existence, regularity and stability in the norm for some neutral partial functional differential equations in fading memory spaces
 Pseudo almost periodic solutions of class in the norm under the light of measure theory
 Global stability for a delay SIR epidemic model with general incidence function, observers design
 Threshold parameters of stochastic SIR and SIRS epidemic models with delay and nonlinear incidence
 Weak solutions for nonlinear BoltzmannPoisson system modeling electron electron interactions.
5. Analytic partial differential equations [2022]
 Treves, Francois, 1930 author.
 Cham : Springer, [2022]
 Description
 Book — xiii, 1228 pages ; 24 cm
 Summary

 Distributions and Analyticity in Euclidean Space
 Functions and Differential Operators in Euclidean Space
 Basic Notation and Terminology
 Smooth, Realanalytic, Holomorphic Functions
 Differential Operators with Smooth Coefficients
 Distributions in Euclidean Space
 Basics on Distributions in Euclidean Space
 Sobolev Spaces
 Distribution Kernels
 Fundamental Solutions, Parametrix, Hypoelliptic PDOs
 Analytic Tools in Distribution Theory
 Analytic Parametrices, Analytic Hypoellipticity
 Ehrenpreisʼ Cutoffs and Analytic Regularity of Distributions
 Distribution Boundary Values of Holomorphic Functions
 The FBI Transform of Distributions : An Introduction
 The Analytic WaveFront Set of a Distribution
 Analyticity of Solutions of Linear PDEs : Basic Results
 Analyticity of Solutions of Elliptic Linear PDEs
 Degenerate Elliptic Equations : Influence of Lower Order Terms
 A Generalization of the Harmonic Oscillator
 Appendix : Hermite's Functions and the Schwartz Space
 The CauchyKovalevskaya Theorem
 A Nonlinear Ovsyannikov Theorem
 Application : the Nonlinear CauchyKovalevskaya Theorem
 Applications to Linear PDE
 Application to Integrodifferential Cauchy Problems
 Hyperfunctions in Euclidean Space
 Analytic Functionals in Euclidean Space
 Analytic Functionals in Complex Domains
 Analytic Functionals in Cn
 Analytic Functionals in Rn as Cohomology Classes
 Hyperfunctions in Euclidean Space
 The Sheaf of Hyperfunctions in Euclidean Space
 Boundary values of holomorphic functions in wedges
 The FBI Transform of Analytic Functionals
 Analytic Wavefront Set of a Hyperfunction
 Edge of the Wedge
 Microfunctions in Euclidean space
 Hyperdifferential Operators
 Action on Holomorphic Functions and on Hyperfunctions
 Local Representation of Hyperfunctions
 Elliptic Hyperdifferential Operators
 Solvability of Constant Coefficients Hyperdifferential Equations
 Geometric Background
 Elements of Differential Geometry
 Regular Manifolds
 Fibre Bundles, Vector Bundles
 Tangent and Cotangent Bundles of a Manifold
 Differential Complexes and Grassman Algebras
 A Primer on Sheaf Cohomology
 Basics on Sheaf Cohomology
 Fine Sheaves and Fine Resolutions
 Relative Sheaf Cohomology
 Edge of the Wedge in (Co)homological Terms
 Distributions and Hyperfunctions on a Manifold
 Distributions and Currents on a Manifold
 Plurisubharmonic functions and pseudoconvex domains
 Hyperfunctions and Microfunctions in an Analytic Manifold
 Lie Algebras of Vector Fields
 The Lie Algebra of Smooth Vector Fields
 Integral Manifolds : Frobeniusʼ Theorem
 Local Flow of a Regular Vector Field
 Foliations Defined By Analytic Vector Fields
 Systems of Vector Fields Generating Special Lie Algebras
 Elements of Symplectic Geometry
 Elements of Symplectic Algebra
 The Metaplectic Group
 Symplectic Manifolds
 Involutive Systems of Functions of Principal Type
 Real and Imaginary Symplectic Structures in C2n
 Real and Imaginary Symplectic Structures on Complex Manifolds
 Stratification of Analytic Varieties and Division of Distributions by Analytic Functions
 Analytic Stratifications
 Analytic Stratifications and Stratifiable Sets
 Analytic Subvarieties
 The Weierstrass Theorems
 Local Partitions of a Complex Hypersurface
 Local Stratifications of a RealAnalytic Variety
 Semianalytic Sets
 Division of Distributions by Analytic Functions
 The Lojasiewicz Inequality
 Division of Distributions by Analytic Functions
 Desingularization and Applications
 Appendix
 Analytic Pseudodifferential Operators and Fourier Integral Operators
 Elementary Pseudodifferential Calculus in the ... Class
 Standard Pseudodifferential Operators
 Symbolic Calculus
 Classical symbols and classical pseudodifferential operators
 The Weyl Calculus in Euclidean Space
 Analytic Pseudodifferential Calculus
 Analytic Pseudodifferential Operators
 Symbolic Calculus
 Analytic Microlocalization In Distribution Theory
 Action on Singularity Hyperfunctions
 Microdifferential Operators
 Fourier Integral Operators
 Fourier Distribution Kernels in Euclidean Space
 The Lagrangian Manifold Associated to a Phasefunction
 Fourier Integral Operators : Basics
 Reduction of the Fiber Variables
 Composition and Continuity of Fourier Integral Operators
 Globally Defined Fourier Integral Operators
 Principles of Analytic Fourier Integral Operators
 Appendix : Stationary Phase Formal Expansion
 Complex Microlocal Analysis
 Classical Analytic Formalism
 Formal Analytic Series
 Classical Analytic Differential Operators of Infinite Order
 The Complex Stationary Phase Formula
 Symbolic Calculus and the KdV Hierarchy
 Germ Fourier Integral Operators in Complex Space
 Analytic Symbols
 Contours and Function Spaces
 Sjöstrand Pairs
 Germ Fourierlike Transforms
 Sjöstrand Triads and Germ Fourier Integral Operators
 Germ Pseudodifferential Operators in Complex Space
 Germ Pseudodifferential Operators
 Classical Germ Pseudodifferential Operators
 Action on distributions
 Action on Hyperfunctions and Microfunctions
 Germ FBI Transforms
 Germ FBI Transforms
 Germ FBI Transforms of Distributions
 The Equivalence Theorem for Distributions
 Analytic Pseudodifferential Operators of Principal Type
 Analytic PDEs of Principal Type : Local Solvability
 Pseudodifferential Operators of Principal Type
 Local Solvability of Analytic PDEs of Principal Type
 Analytic PDEs of Principal Type : Regularity of the Solutions
 A New Concept : Subellipticity
 Statement of the Main Theorem
 Hypoellipticity Implies (Q)
 Property (Q) Implies Subellipticity
 Analytic Hypoellipticity Implies (Q)
 Property (Q) Implies Analytic Hypoellipticity
 The ... Situation
 Propagation of Analytic Singularities
 Appendix : Properties of Real Polynomials in a Single Variable
 Appendix : Analytic Estimates of Exponential Amplitudes
 Solvability of Constant Vector Fields of Type (1,0)
 CConvexity and Global Solvability
 Local Solvability at the Boundary : First Steps
 Local Solvability at the Boundary : Final Characterization
 The Differential Complex : Generalities
 Appendix : Minima of Families of Plurisubharmonic Functions
 Pseudodifferential Solvability and Property (...)
 Solvability : the Difference between Differential and Pseudodifferential
 Property (...)
 Microlocal Solvability in Distributions
 Pseudodifferential Complexes in Tube Structures
 Pseudodifferential Complexes of Principal Type
 Tube Pseudodifferential Complexes
 Phasefunction and Amplitude
 Approximate Homotopy Formulas
 Homotopy Formulas
 Poincaré Lemmas
 References
 Notation Index
 Index
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QA374 .T684 2022  Unknown 
 Partielle Differenzialgleichungen. English
 Arendt, Wolfgang, 1950 author.
 Cham : Springer, 2022.
 Description
 Book — 1 online resource (1 volume) : illustrations (black and white)
 Summary

 1 Modeling, or where do differential equations come from. 2 Classification and characteristics. 3 Elementary methods. 4 Hilbert spaces. 5 Sobolev spaces and boundary value problems in dimension one. 6 Hilbert space methods for elliptic equations. 7 Neumann and Robin boundary conditions. 8 Spectral decomposition and evolution equations. 9 Numerical methods. 10 Maple (R), or why computers can sometimes help. Appendix.
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 Salsa, S., author.
 Fourth edition.  Cham : Springer, [2022]
 Description
 Book — 1 online resource (xviii, 677 pages) : illustrations.
 Summary

 1 Introduction. 2 Diffusion. 3 The Laplace Equation. 4 Scalar Conservation Laws and First Order Equations. 5 Waves and Vibration. 6 Elements of Functional Analysis. 7 Distributions and Sobolev Spaces. 8 Variational Formulation of Elliptic Problems. 9 Weak Formulation of Evolution Problems. 10 More Advanced Topics. 11 Systems of Conservation Laws. Appendix A: Measures and Integrals. Appendix B: Identities and Formulas.
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 Singapore : Springer, 2022.
 Description
 Book — 1 online resource : illustrations (black and white, and color).
 Summary

 Part I: Longtime behavior of NLStype equations. 1 Scipio Cuccagna, Note on small data soliton selection for nonlinear Schroedinger equations with potential. 2 Jacopo Bellazzini and Luigi Forcella, Dynamics of solutions to the GrossPitaevskii equation describing dipolar BoseEinstein condensates. Part II: Probabilistic and nonstandard methods in the study of NLS equations. 3 Renato Luca, Almost sure pointwise convergence of the cubic nonlinear Schroedinger equation on T^2. 4 Nevena Dugandzija and Ivana Vojnovic, Nonlinear Schroedinger equation with singularities. Part III: Dispersive properties. 5 Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone, Schroedinger flow's dispersive estimates in a regime of rescaled potentials. 6 Federico Cacciafesta, Eric Sere, Junyong Zhang, Dispersive estimates for the DiracCoulomb equation. 7 Matteo Gallone, Alessandro Michelangeli, Eugenio Pozzoli, Heat equation with inversesquare potential of bridging type across two halflines. Part IV: Wave and Kdvtype equations. 8 Felice Iandoli, On the Cauchy problem for quasilinear Hamiltonian KdVtype equations. 9 Vladimir Georgiev and Sandra Lucente, Linear and nonlinear interaction for wave equations with time variable coefficients. 10 Matteo Gallone and Antonio Ponno, Hamiltonian field theory close to the wave equation: from FermiPastaUlam to water waves.
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9. Partial differential equations in anisotropic MusielakOrlicz spaces [electronic resource] [2021]
 Chlebicka, Iwona, author.
 Cham, Switzerland : Springer, 2021.
 Description
 Book — 1 online resource Digital: text file.PDF.
 Summary

 Part I Overture:
 1. Introduction.
 2. NFunctions.
 3. MusielakOrlicz Spaces. Part II PDEs:
 4. Weak Solutions.
 5. Renormalized Solutions.
 6. Homogenization of Elliptic Boundary Value Problems.
 7. NonNewtonian Fluids. Part III Auxiliaries:
 8. Basics.
 9. Functional Inequalities. References. List of Symbols. Index. .
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(source: Nielsen Book Data)
 Beijing, China : Higher Education Press Limited Company ; Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2019]
 Description
 Book — 1 online resource.
 Summary

 Intro; Contents; Preface; Control of Partial Differential Equations: Theoretical Aspects;
 1. Introduction;
 2. Introduction to Controllability; 2
 .1. Approximate Controllability; 2
 .2. Null Controllability; 2
 .3. Exact Controllability; 2
 .4. Exact Controllability to Trajectories;
 3. Simple Examples; 3
 .1. Transport Equation in 1D; 3
 .2. Wave Equation in 1D;
 4. Exact Controllability for the Wave Equation; 4
 .1. Exact Controllability for Boundary Control; 4
 .2. Case of Distributed Control;
 5. Controllability of Schrödinger Equation; 5
 .1. Schrödinger Equation; 5
 .2. Controllability Results
 6. Controllability of Linear Diffusion Convection Equations6
 .1. Statement of the Problem and Result; 6
 .2. An Auxiliary Optimal Control Problem; 6
 .3. Null Controllability Modulo Observability Inequality; 6
 .4. Global Carleman Inequality; 6.4
 .1. Weight Functions; 6.4
 .2. Proof of a Global Carleman Inequality; 6.4
 .3. Case of a General DiffusionConvection Operator; 6
 .5. Observability Inequality; 6
 .6. Another Strategy; Bibliography; Control of Partial Differential Equations: Numerical Aspects;
 1. Introduction;
 2. Controllability of FiniteDimensional Linear Systems; 2
 .1. Introduction
 2
 .2. FiniteDimensional Case, First Comments2
 .3. Examples; 2
 .4. Duality Techniques; 2
 .5. Observability Property; 2
 .6. Comments on the Control Map; 2
 .7. Kalman Rank Condition; 2
 .8. A Data Assimilation Problem;
 3. The Wave Equation; 3
 .1. The Continuous Setting; 3.1
 .1. Functional Setting; 3.1
 .2. Control and Observability Results; 3
 .2. The Discrete Wave Equation: The Naive Approach; 3.2
 .1. Setting; 3.2
 .2. Existence of the Discrete NullControls; 3.2
 .3. Numerical Experiments; 3.2
 .4. Lack of Uniform Observability; 3.2
 .5. Blow up of Discrete Controls; 3
 .3. Remedies
 3.3
 .1. A Fourier Filtering Technique3.3
 .2. Designing a Mesh Guaranteeing Uniform Observability Properties; 3
 .4. Further Comments; 3.4
 .1. Higher Dimensions; 3.4
 .2. The Effect of TimeDiscretization; 3.4
 .3. Rate of Convergence of the Discrete Controls;
 4. The Heat Equation; 4
 .1. The Continuous Case; 4
 .2. Difficulties of Computing Numerical Controls for the Heat Equation; 4
 .3. A Remedy; 4
 .4. Further Comments; Bibliography; Complex Geometrical Optics and Calderón's Problem;
 0. Introduction;
 1. The DirichlettoNeumann Map;
 2. Boundary Determination and Layer Stripping
 3. Complex Geometrical Optics Solutions4. Applications of Complex Geometrical Optics Solutions; 4.1. Uniqueness for Calderón's Problem; 4.2. Determining Cavities; 5. Complex Geometrical Optics Solutions for First Order Perturbations of the Laplacian; 5.1. Intertwining Property (Part 1); 5.2. Intertwining Property (Part 2); 5.3. Intertwining Property (Part 3)
 Some Reductions; 5.4. Construction of Pseudoanalytic Matrices; Bibliography; A MiniCourse on Stochastic Control; 1. Introduction; 2. Some Preliminary Results from Probability Theory and Stochastic Analysis
(source: Nielsen Book Data)
11. Partial differential equations arising from physics and geometry : a volume in memory of Abbas Bahri [2019]
 Cambridge : Cambridge University Press, 2019.
 Description
 Book — xvi, 453 pages : illustrations ; 23 cm.
 Summary

 Preface Mohamed Ben Ayed, Mohamed Ali Jendoubi, Yomna Rebai, Hassna Riahi and Hatem Zaag
 Abbas Bahri: a dedicated life Mohamed Ben Ayed
 1. Blowup rate for a semilinear wave equation with exponential nonlinearity in one space dimension Asma Azaiez, Nader Masmoudi and Hatem Zaag
 2. On the role of anisotropy in the weak stability of the NavierStokes system Hajer Bahouri, JeanYves Chemin and Isabelle Gallagher
 3. The motion law of fronts for scalar reactiondiffusion equations with multiple wells: the degenerate case Fabrice Bethuel and Didier Smets
 4. Finitetime blowup for some nonlinear complex GinzburgLandau equations Thierry Cazenave and Seifeddine Snoussi
 5. Asymptotic analysis for the LaneEmden problem in dimension two Francesca de Marchis, Isabella Ianni and Filomena Pacella
 6. A data assimilation algorithm: the paradigm of the 3D Leray model of turbulence Aseel Farhat, Evelyn Lunasin and Edriss S. Titi
 7. Critical points at infinity methods in CR geometry Najoua Gamara
 8. Some simple problems for the next generations Alain Haraux
 9. Clustering phenomena for linear perturbation of the Yamabe equation Angela Pistoia and Giusi Vaira
 10. Towards better mathematical models for physics Luc Tartar.
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QA377 .P378 2019  Unknown 
12. Topics in partial differential equations [2019]
 Gupta, Parmanand, author.
 First edition.  Bengaluru : Firewall Media, an imprint of Laxmi Publications Pvt. Ltd., 2019.
 Description
 Book — 1 online resource
 Kavallaris, Nikos I.
 Cham : Springer, [2018]
 Description
 Book — 1 online resource. Digital: text file; PDF.
 Summary

 Dedication. Preface. Acknowledgements. Part I Applications in Engineering. Microelectromechanicalsystems(MEMS). Ohmic Heating Phenomena. Linear Friction Welding. Resistance Spot Welding. Part II Applications in Biology. GiererMeinhardt System. A Nonlocal Model Illustrating Replicator Dynamics. A Nonlocal Model Arising in Chemotaxis. A Nonlocal ReactionDiffusion System Illustrating Cell Dynamics. Appendices. Index.
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14. Analytical methods for Kolmogorov equations [2017]
 Lorenzi, Luca, author.
 Second edition  Boca Raton, Florida : CRC Press, [2017]
 Description
 Book — 1 online resource
 Summary

 1. Autonomous Kolmogorov equations
 2. Nonautonomous Kolmogorov equations
 3. Appendices
 Schönlieb, CarolaBibiane, author.
 Cambridge : Cambridge University Press, 2015.
 Description
 Book — 1 online resource : digital, PDF file(s).
 Summary

 1. Introduction
 2. Overview of mathematical inpainting methods
 3. The principle of good continuation
 4. Secondorder diffusion equations for inpainting
 5. Higherorder PDE inpainting
 6. Transport inpainting
 7. The MumfordShah image for inpainting
 8. Inpainting mechanisms of transport and diffusion
 9. Applications.
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 Shearer, Michael, author.
 Princeton : Princeton University Press, [2015]
 Description
 Book — x, 274 pages : illustrations ; 26 cm
 Summary

This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors.
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QA374 .S45 2015  Unknown 
 Rădulescu, Vicenţiu D., 1958 author.
 Boca Raton, FL : CRC Press, [2015]
 Description
 Book — xxi, 301 pages : illustrations ; 24 cm.
 Summary

 Isotropic and Anisotropic Function Spaces Lebesgue and Sobolev Spaces with Variable Exponent History of function spaces with variable exponent Lebesgue spaces with variable exponent Sobolev spaces with variable exponent Dirichlet energies and EulerLagrange equations Lavrentiev phenomenon Anisotropic function spaces Orlicz spaces
 Variational Analysis of Problems with Variable Exponents Nonlinear Degenerate Problems in NonNewtonian Fluids Physical motivation A boundary value problem with nonhomogeneous differential operator Nonlinear eigenvalue problems with two variable exponents A sublinear perturbation of the eigenvalue problem associated to the Laplace operator Variable exponents versus Morse theory and local linking The CaffarelliKohnNirenberg inequality with variable exponent
 Spectral Theory for Differential Operators with Variable Exponent Continuous spectrum for differential operators with two variable exponents A nonlinear eigenvalue problem with three variable exponents and lack of compactness Concentration phenomena: the case of several variable exponents and indefinite potential Anisotropic problems with lack of compactness and nonlinear boundary condition
 Nonlinear Problems in OrliczSobolev Spaces Existence and multiplicity of solutions A continuous spectrum for nonhomogeneous operators Nonlinear eigenvalue problems with indefinite potential Multiple solutions in OrliczSobolev spaces Neumann problems in OrliczSobolev spaces
 Anisotropic Problems: Continuous and Discrete Anisotropic Problems Eigenvalue problems for anisotropic elliptic equations Combined effects in anisotropic elliptic equations Anisotropic problems with noflux boundary condition Bifurcation for a singular problem modelling the equilibrium of anisotropic continuous media
 Difference Equations with Variable Exponent Eigenvalue problems associated to anisotropic difference operators Homoclinic solutions of difference equations with variable exponents Lowenergy solutions for discrete anisotropic equations
 Appendix A: Ekeland Variational Principle Appendix B: Mountain Pass Theorem Bibliography Index A Glossary is included at the end of each chapter.
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QA377 .R33 2015  Unknown 
18. Introduction to partial differential equations for scientists and engineers using Mathematica [2014]
 Adzievski, Kuzman, author.
 Boca Raton, FL : CRC Press, [2014]
 Description
 Book — xiii, 634 pages : illustrations ; 25 cm
 Summary

 Fourier Series The Fourier Series of a Periodic Function Convergence of Fourier Series Integration and Differentiation of Fourier Series Fourier Sine and Fourier Cosine Series Mathematica Projects Integral Transforms The Fourier Transform and Elementary Properties Inversion Formula of the Fourier Transform Convolution Property of the Fourier Transform The Laplace Transform and Elementary Properties Differentiation and Integration of the Laplace Transform Heaviside and Dirac Delta Functions Convolution Property of the Laplace Transform Solution of Differential Equations by the Integral Transforms The SturmLiouville Problems Regular SturmLiouville Problem Eigenvalues and Eigenfunctions Eigenfunction Expansion Singular SturmLiouville Problem: Legendre's Equation Singular SturmLiouville Problem: Bessel's Equation Partial Differential Equations Basic Concepts and Definitions Formulation of Initial and Boundary Problems Classification of Partial Differential Equations Some Important Classical Linear Partial Differential Equations The Principle of Superposition First Order Partial Differential Equations Linear Equations with Constant Coefficients Linear Equations with Variable Coefficients First Order NonLinear Equations Cauchy's Method of Characteristics Mathematica Projects Hyperbolic Partial Differential Equations The Vibrating String and Derivation of the Wave Equation Separation of Variables for the Homogeneous Wave Equation D'Alambert's Solution of the Wave Equation Inhomogeneous Wave Equations Solution of the Wave Equation by Integral Transforms Two Dimensional Wave Equation: Vibrating Membrane The Wave Equation in Polar and Spherical Coordinates Numerical Solutions of the Wave Equation Mathematica Projects Parabolic Partial Differential Equations Heat Flow and Derivation of the Heat Equation Separation of Variables for the One Dimensional Heat Equation Inhomogeneous Heat Equations Solution of the Heat Equation by Integral Transforms Two Dimensional Heat Equation The Heat Equation in Polar and Spherical Coordinates Numerical Solutions of the Heat Equation Mathematica Projects Elliptic Partial Differential Equations The Laplace and Poisson Equations Separation of Variables for the Laplace Equation The Laplace Equation in Polar and Spherical Coordinates Poisson Integral Formula Numerical Solutions of the Laplace Equation Mathematica Projects Appendix A. Special Functions Appendix B. Table of the Fourier Transform of Some Functions Appendix C. Table of the Laplace Transform of Some Functions.
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QA377 .A47 2014  Unknown 
19. Partial differential equations [2013]
 Jost, Jürgen, 1956
 Third edition.  New York : Springer, c2013.
 Description
 Book — xiii, 410 pages ; 24 cm.
 Summary

 Preface. Introduction: What are Partial Differential Equations?. 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order. 2 The Maximum Principle. 3 Existence Techniques I: Methods Based on the Maximum Principle. 4 Existence Techniques II: Parabolic Methods. The Heat Equation. 5 ReactionDiffusion Equations and Systems. 6 Hyperbolic Equations. 7 The Heat Equation, Semigroups, and Brownian Motion. 8 Relationships between Different Partial Differential Equations. 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III). 10 Sobolev Spaces and L^2 Regularity theory. 11 Strong solutions. 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV). 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash. Appendix: Banach and Hilbert spaces. The L^pSpaces. References. Index of Notation. Index.
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QA377 .J66 2013  Unknown 
 Basel : Birkhäuser, c2011
 Description
 Book — vi, 367 p. : ill. ; 24 cm.
 Summary

 Toeplitz operators and asymptotic equivariant index / L. Boutet de Monvel
 Boundary value problems of analytic and harmonic functions in a domain with piecewise smooth boundary in the frame of variable exponent Lebesgue spaces / V. Kokilashvili
 Edgedegenerate operators at conical exits to infinity / B.W. Schulze
 On a method for solving boundary problems for a thirdorder equation with multiple characteristics / Y.P. Apakov
 On stability and trace regularity of solutions to ReissnerMindlinTimoshenko equations / G. Avalos and D. Toundykov
 Linearization of a coupled system of nonlinear elasticity and viscous fluid / L. Bociu and J.P. Zolésio
 Some results of the identification of memory kernels / F. Colombo and D. Guidetti
 A kuniform maximum principle when 0 is an eigenvalue / G. Fragnelli and D. Mugnai
 Steadystate solutions for a general brusselator system / M. Ghergu
 Ordinary differential equations with distributions as coefficients in the sense of the theory of new generalized functions / U.U. Hrusheuski
 A boundary condition and spectral problems for the Newton potential / T.Sh. Kalmenov and D. Suragan
 An extremum principle for a class of hyperbolic type equations and for operators connected with them / I.U. Khaydarov, M.S. Salakhitdinov and A.K. Urinov
 Numerical investigations of tangled flows in a channel of constant and variable section at presence of recirculation zone / S. Khodjiev
 The optimal interior regularity for the critical case of a clamped thermoelastic system with point control revisited / C. Lebiedzik and R. Triggiani
 Multidimensional controllability problems with memory / P. Loreti and D. Sforza
 The Schrödinger flow in a compact manifold: highfrequency dynamics and dispersion / F. Macià
 Optimality of the asymptotic behavior of the energy for wave models / M. Reissig
 On singular systems of parabolic functional equations / L. Simon
 Boundaryvalue problems for a class of thirdorder composite type equations / O.S. Zikirov
 Shapemorphic metric, geodesic stability / J.P. Zolésio.
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QA374 .M76 2011  Unknown 
21. Partial differential equations [2011 ]
 Taylor, Michael E., 1946
 2nd ed.  New York : Springer, c2011
 Description
 Book — v. : ill. ; 24 cm.
 Summary

 1. Basic theory
 2. Qualitative studies of linear equations
 3. Nonlinear equations.
(source: Nielsen Book Data)
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
(source: Nielsen Book Data)
The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of CalderonZygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis.
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QA374 .T392 2011 V.1  Unknown Request 
QA374 .T392 2011 V.2  Unknown 
QA374 .T392 2011 V.3  Unknown 
22. Partial differential equations [2010]
 Evans, Lawrence C., 1949
 2nd ed.  Providence, R.I. : American Mathematical Society, 2010.
 Description
 Book — 749 p. ; 26 cm.
 Summary

This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail...Evans' book is evidence of his mastering of the field and the clarity of presentation (Luis Caffarelli, University of Texas) It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations ...Every graduate student in analysis should read it. (David Jerison, MIT) I use Partial Differential Equations to prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's ...I am very happy with the preparation it provides my students. (Carlos Kenig, University of Chicago) Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge ...An outstanding reference for many aspects of the field. (Rafe Mazzeo, Stanford University.
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23. Partial differential equations [2010]
 Evans, Lawrence C., 1949 author.
 2nd ed  Providence, R.I. : American Mathematical Society, [2010]
 Description
 Book — 1 online resource (xv, 712 pages) : illustrations
 Summary

 Part I. Representation formulas for solutions
 Four important linear PDE
 Nonlinear firstorder PDE
 Other ways to represent solutions
 Part II. Theory for linear partial differential equations
 Sobolev spaces
 Secondorder elliptic equations
 Linear evolution equations
 Part III. Theory for nonlinear partial differential equations
 The calculus of variations
 Nonvariational techniques
 HamiltonJacobi equations
 Systems of conservation laws
 Nonlinear wave equations
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24. Analytical and numerical aspects of partial differential equations : notes of a lecture series [2009]
 Berlin ; New York : Walter De Gruyter, c2009.
 Description
 Book — 290 p. : ill. ; 25 cm.
 Summary

This text contains a series of selfcontained reviews on the state of the art in different areas of partial differential equations, presented by French mathematicians. Topics include qualitative properties of reactiondiffusion equations, multiscale methods coupling atomistic and continuum mechanics, adaptive semiLagrangian schemes for the VlasovPoisson equation, and coupling of scalar conservation laws.
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25. Handbook of differential equations [electronic resource] : stationary partial differential equations [2008]
 Chipot, M. (Michel)
 Oxford : Elsevier, 2008.
 Description
 Book — p. cm.
 Summary

 1. Semilinear elliptic systems: existence, multiplicity, symmetry of solutions (D.G. De Figueiredo)
 2. Nonlinear variational problems via the fibering method (S. Pohozaev)
 3. Superlinear elliptic equations and systems (B. Ruf)
 4. Nonlinear eigenvalue problem with quantization (T. Suzuki and F. Takahashi)
 5. Stationary problem of Boltzmann equation (S. Ukai and T Yang)
 6. Existence and stability of spikes for the GiererMeinhardt system (J. Wei).
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26. Handbook of differential equations [electronic resource] : stationary partial differential equations [2008]
 Oxford : Elsevier, 2008.
 Description
 Book
 Summary

 1. Domain Perturbation for Linear and SemiLinear Boundary Value Problems, D. Daners.
 2. Singular solutions of semilinear elliptic problems J. D̀vila.
 3. Positive solutions to semi linear and quasilinear elliptic equations on unbounded domains, V. Kondratiev, V. Liskevich and Z. Sobol.
 4. Symmetry of solutions of elliptic equations via maximum principles, F. Pacella and M. Ramaswamy.
 5. Stationary Boundary Value Problems for Compressible NavierStokes equations, P.I. Plotnikov and J. Sokolowski.
 6. Positive Solutions for LotkaVolterra Systems with Cross Diffusion, Y. Yamada.
 7. Fixed Point Theory and Elliptic Boundary Value Problems, H. Zou.
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This is a collection of self contained stateofthe art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching. Written by wellknown experts in the field, this is a self contained volume in series covering one of the most rapid developing topics in mathematics. It is well informed and thoroughly updated for students, academics and researchers.
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 Strauss, Walter A., 1937
 2nd ed.  Hoboken, N.J. ; Chichester : Wiley, 2008.
 Description
 Book — x, 454 p. : ill. ; 24 cm.
 Summary

 Chapter 1: Where PDEs Come From 1.1 What is a Partial Differential Equation? 1.2 FirstOrder Linear Equations 1.3 Flows, Vibrations, and Diffusions 1.4 Initial and Boundary Conditions 1.5 WellPosed Problems 1.6 Types of SecondOrder Equations
 Chapter 2: Waves and Diffusions 2.1 The Wave Equation 2.2 Causality and Energy 2.3 The Diffusion Equation 2.4 Diffusion on the Whole Line 2.5 Comparison of Waves and Diffusions
 Chapter 3: Reflections and Sources 3.1 Diffusion on the HalfLine 3.2 Reflections of Waves 3.3 Diffusion with a Source 3.4 Waves with a Source 3.5 Diffusion Revisited
 Chapter 4: Boundary Problems 4.1 Separation of Variables, The Dirichlet Condition 4.2 The Neumann Condition 4.3 The Robin Condition
 Chapter 5: Fourier Series 5.1 The Coefficients 5.2 Even, Odd, Periodic, and Complex Functions 5.3 Orthogonality and the General Fourier Series 5.4 Completeness 5.5 Completeness and the Gibbs Phenomenon 5.6 Inhomogeneous Boundary Conditions
 Chapter 6: Harmonic Functions 6.1 Laplace's Equation 6.2 Rectangles and Cubes 6.3 Poisson's Formula 6.4 Circles, Wedges, and Annuli
 Chapter 7: Green's Identities and Green's Functions 7.1 Green's First Identity 7.2 Green's Second Identity 7.3 Green's Functions 7.4 HalfSpace and Sphere
 Chapter 8: Computation of Solutions 8.1 Opportunities and Dangers 8.2 Approximations of Diffusions 8.3 Approximations of Waves 8.4 Approximations of Laplace's Equation 8.5 Finite Element Method
 Chapter 9: Waves in Space 9.1 Energy and Causality 9.2 The Wave Equation in SpaceTime 9.3 Rays, Singularities, and Sources 9.4 The Diffusion and Schrodinger Equations 9.5 The Hydrogen Atom
 Chapter 10: Boundaries in the Plane and in Space 10.1 Fourier's Method, Revisited 10.2 Vibrations of a Drumhead 10.3 Solid Vibrations in a Ball 10.4 Nodes 10.5 Bessel Functions 10.6 Legendre Functions 10.7 Angular Momentum in Quantum Mechanics
 Chapter 11: General Eigenvalue Problems 11.1 The Eigenvalues Are Minima of the Potential Energy 11.2 Computation of Eigenvalues 11.3 Completeness 11.4 Symmetric Differential Operators 11.5 Completeness and Separation of Variables 11.6 Asymptotics of the Eigenvalues
 Chapter 12: Distributions and Transforms 12.1 Distributions 12.2 Green's Functions, Revisited 12.3 Fourier Transforms 12.4 Source Functions 12.5 Laplace Transform Techniques
 Chapter 13: PDE Problems for Physics 13.1 Electromagnetism 13.2 Fluids and Acoustics 13.3 Scattering 13.4 Continuous Spectrum 13.5 Equations of Elementary Particles
 Chapter 14: Nonlinear PDEs 14.1 Shock Waves 14.2 Solitions 14.3 Calculus of Variations 14.4 Bifurcation Theory 14.5 Water WavesAppendix A.1 Continuous and Differentiable Functions A.2 Infinite Sets of Functions A.3 Differentiation and Integration A.4 Differential Equations A.5 The Gamma FunctionReferencesAnswers and Hints to Selected ExercisesIndex.
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QA374 .S86 2008  Unknown 
QA374 .S86 2008  Unknown 
QA374 .S86 2008  Unknown 
 Levandosky, Julie.
 2nd ed.  Danvers, MA : John Wiley & Sons, 2008.
 Description
 Book — vii, 215 p. : ill. ; 28 cm.
 Online
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QA374 .L49 2008  Unknown Request 
QA374 .L49 2008  Unknown 
QA374 .L49 2008  Unknown 
29. Partial differential equations [2007]
 Jost, Jürgen, 1956
 2nd ed.  New York : Springer, c2007.
 Description
 Book — xiii, 356 p. : ill. ; 25 cm.
 Summary

 The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order. The maximum principle. Existence techniques I: methods based on the maximum principle. Existence techniques II: Parabolic methods. The Heat equation. Reaction Diffusion Equations and Systems. The wave equation and its connections with the Laplace and heat equations. The heat equation, semigroups, and Brownian motion. The Dirichlet principle. Variational methods for the solution of PDEs (Existence techniques III). Sobolev spaces and L2 regularity theory. Strong solutions. The regularity theory of Schauder and the continuity method (Existence techniques IV). The Moser iteration method and the reqularity theorem of de Giorgi and Nash. Appendix: Banach and Hilbert spaces. The Lpspaces. References. Index of Notation. Index.
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QA377 .J66 2007  Unknown 
 Jost, Jürgen, 1956
 2nd ed.  New York : Springer, c2007.
 Description
 Book — xiii, 356 p. : ill.
 Ying, Long'an, 1936
 Singapore ; Hackensack, N.J. : World Scientific, c2006.
 Description
 Book — ix, 269 : ill.
 Summary

 Exterior Problems of Partial Differential Equations
 Boundary Element Method
 Infinite Element Method
 Artificial Boundary Conditions
 Perfectly Matched Layer Method
 Spectral Method.
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 Zauderer, Erich.
 3rd ed.  Hoboken, N.J. : WileyInterscience, c2006.
 Description
 Book — xxvii, 930 p. : ill. ; 25 cm.
 Summary

 Preface.
 1. Random Walks and Partial Differential Equations.
 2. First Order Partial Differential Equations.
 3. Classification of Equations and Characteristics.
 4. Initial and Boundary Value Problems in Bounded Regions.
 5. Integral Transforms.
 6. Integral Relations.
 7. Green's Functions.
 8. variational and Other Methods.
 9. Regular Perturbation Methods.
 10. Asymptotic Methods.
 11. Finite Difference Methods.
 12. Finite Element Methods in Two Dimensions. Bibliography. Index.
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QA377 .Z38 2006  Unknown 
 Providence, R.I. : American Mathematical Society, c2006.
 Description
 Book — viii, 123 p. : ill. ; 26 cm.
 Summary

 Steepest descent flows and applications to spaces of probability measures by L. Ambrosio Hypocoercivity: the example of linear transport by L. Desvillettes A hybrid system of PDE's arising in multistructure interaction: Coupling of wave equations in $n$ and $n1$ space dimensions by H. Koch and E. Zuazua Some rigorous results for vortex patterns in BoseEinstein condensates by A. Aftalion Qualitative properties of some Boltzmann like equations which do not fulfill a detailed balance condition by M. Escobedo and S. Mischler.
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QA374 .R4235 2006  Available 
 Salsa, S.
 Milano : Springer, 2005.
 Description
 Book — viii, 406 p. : ill.
35. Hypoelliptic Estimates and Spectral Theory for FokkerPlanck Operators and Witten Laplacians [2005]
 Helffer, Bernard.
 1862th ed.  Berlin : Springer, 2005.
 Description
 Book — 1 online resource (210 pages)
 Summary

 1. Introduction.
 2. Kohn's Proof of the Hypoellipticity of the Hoermander Operators.
 3. Compactness Criteria for the Resolvent of Schroedinger Operators.
 4. Global Pseudodifferential Calculus.
 5. Analysis of some FokkerPlanck Operator.
 6. Return to Equillibrium for the FokkerPlanck Operator.
 7. Hypoellipticity and nilpotent groups.
 8. Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts.
 9. On FokkerPlanck Operators and Nilpotent Techniques.
 10. Maximal Microhypoellipticity for Systems and Applications to Witten Laplacians.
 11. Spectral Properties of the WittenLaplacians in Connection with Poincare inequalities for Laplace Integrals.
 12. Semiclassical Analysis for the Schroedinger Operator: Harmonic Approximation.
 13. Decay of Eigenfunctions and Application to the Splitting.
 14. Semiclassical Analysis and Witten Laplacians: Morse Inequalities.
 15. Semiclassical Analysis and Witten Laplacians: Tunneling Effects.
 16. Accurate Asymptotics for the Exponentially Small Eigenvalues of the Witten Laplacian.
 17. Application to the FokkerPlanck Equation.
 18. Epilogue. References. Index.
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36. Introduction to partial differential equations [electronic resource] : a computational approach [2005]
 Tveito, Aslak, 1961
 Corr. 2nd print.  Berlin ; New York : Springer, c2005.
 Description
 Book — xv, 392 p. : ill.
 Renardy, Michael.
 2nd ed.  New York : Springer, c2004.
 Description
 Book — xiv, 434 p. : ill. ; 25 cm.
 Summary

 Introduction* Characteristics* Classification of Characteristics * Conservation Laws and Shocks* Maximum Principles* Distributions* Function Spaces* Sobolev Spaces * Operator Theory * Linear Elliptic Equations * Nonlinear Elliptic Equations * Energy Methods for Evolution Problems * Semigroup Methods * References * Index.
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QA374 .R4244 2004  Unknown 
38. Partial differential equations and systems not solvable with respect to the highestorder derivative [2003]
 Uravnenii͡a i sistemy, ne razreshennye otnositelʹno starsheĭ proizvodnoĭ. English
 Demidenko, G. V. (Gennadiĭ Vladimirovich)
 New York : Marcel Dekker, c2003.
 Description
 Book — xvi, 490 p : port. ; 24 cm.
 Summary

 Preliminaries the Cauchy problem for equations not solved relative to the higherorder derivative
 the Cauchy problem for nonCauchyKovalevskaya type systems
 mixed problems in the quarter of the space
 qualitative properties of solutions toSobolevtype equations. Appendices: S.L. Sobolev  on a new problem in mathematical physics
 bibliographic comments
 literature.
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QA374 .D46 2003  Available 
 McOwen, Robert C.
 2nd ed.  Upper Saddle, N.J. : Prentice Hall, c2003.
 Description
 Book — xii, 452 p. : ill. ; 24 cm.
 Summary

 Introduction.
 1. FirstOrder Equations.
 2. Principles for HigherOrder Equations.
 3. The Wave Equation.
 4. The Laplace Equation.
 5. The Heat Equation.
 6. Linear Functional Analysis.
 7. Differential Calculus Methods.
 8. Linear Elliptic Theory.
 9. Two Additional Methods.
 10. Systems of Conservation Laws.
 11. Linear and Nonlinear Diffusion.
 12. Linear and Nonlinear Waves.
 13. Nonlinear Elliptic Equations. Appendix on Physics. Hints and Solutions for Selected Exercises. References. Index. Index of Symbols.
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QA377 .M323 2003  Unknown 
40. Partial differential equations [2002]
 Jost, Jürgen, 1956
 New York : Springer, c2002.
 Description
 Book — xi, 325 p. : ill. ; 24 cm.
 Summary

 Introduction. The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order. The maximum principle. Existence techniques I: methods based on the maximum principle. Existence techniques II: Parabolic methods. The Head equation. The wave equation and its connections with the Laplace and heat equation. The heat equation, semigroups, and Brownian motion. The Dirichlet principle. Variational methods for the solution of PDE (Existence techniques III). Sobolev spaces and L2 regularity theory. Strong solutions. The regularity theory of Schauder and the continuity method (Existence techniques IV). The Moser iteration method and the reqularity theorem of de Giorgi and Nash. Banach and Hilbert spaces. The Lpspaces. Bibliography.
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QA377 .J66 2002  Unknown 
 Taylor, Michael E., 1946
 Providence, RI : American Mathematical Society, 2000.
 Description
 Book — 1 online resource (x, 257 p).
 Summary

 1. Pseudodifferential operators with mildly regular symbols 2. Paradifferential operators and nonlinear estimates 3. Applications to PDE 4. Layer potentials on Lipschitz surfaces
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42. Tools for PDE : pseudodifferential operators, paradifferential operators, and layer potentials [2000]
 Taylor, Michael E., 1946
 Providence, RI : American Mathematical Society, 2000.
 Description
 Book — x, 257 p. ; 27 cm.
 Summary

This book develops three related tools that are useful in the analysis of partial differential equations, arising from the classical study of singular integral operators: pseudodifferential operators, paradifferential operators, and layer potentials. A theme running throughout the work is the treatment of PDE in the presence of relatively little regularity. The first chapter studies classes of pseudodifferential operators whose symbols have a limited degree of regularity; the second chapter shows how paradifferential operators yield sharp estimates on the action of various nonlinear operators on function spaces. The third chapter applies this material to an assortment of results in PDE, including regularity results for elliptic PDE with rough coefficients, planar fluid flows on rough domains, estimates on Riemannian manifolds given weak bounds on Ricci tensor, divcurl estimates, and results on propagation of singularities for wave equations with rough coefficients. The last chapter studies the method of layer potentials on Lipschitz domains, concentrating on applications to boundary problems for elliptic PDE with variable coefficients. Michael Taylor is the author of several wellknown books on topics in PDEs and pseudodifferential operators. His Noncommutative Harmonic Analysis, Volume 22 in the Mathematical Surveys and Monographs series published by the AMS, is a good introduction to the use of Lie groups in linear analysis and PDEs. The present book, Tools for PDE, is suitable as a text for advanced graduate students preparing to concentrate in PDE and/or harmonic analysis.
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43. Beginning partial differential equations [1999]
 O'Neil, Peter V.
 New York : Wiley, c1999.
 Description
 Book — x, 500 p. : ill. ; 24 cm.
 Summary

 First Order Partial Differential Equations. Linear Second Order Partial Differential Equations. Elements of Fourier Analysis. The Wave Equation. The Heat Equation. Dirichlet and Neumann Problems. Conclusion. Index.
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QA377 .O54 1999  Unknown 
44. Introduction to partial differential equations [electronic resource] : a computational approach [1998]
 Tveito, Aslak, 1961
 New York : Springer, c1998.
 Description
 Book — xv, 392 p. : ill.
45. Partial differential equations [1998]
 Evans, Lawrence C., 1949
 Providence, R.I. : American Mathematical Society, c1998.
 Description
 Book — xvii, 662 p. : ill. ; 26 cm.
 Summary

 Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear firstorder PDE Other ways to represent solutions Part II: Theory for linear partial differential equations: Sobolev spaces Secondorder elliptic equations Linear evolution equations Part III: Theory for nonlinear partial differential equations: The calculus of variations Nonvariational techniques HamiltonJacobi equations Systems of conservation laws Appendices Bibliography Index.
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46. Partial differential equations [1991]
 Rauch, Jeffrey, author.
 Corrected second printing.  New York, NY : Springer, 1997.
 Description
 Book — 1 online resource (x, 266 pages) Digital: text file.PDF.
 Summary

 1 Power Series Methods. 1
 .1. The Simplest Partial Differential Equation. 1
 .2. The Initial Value Problem for Ordinary Differential Equations. 1
 .3. Power Series and the Initial Value Problem for Partial Differential Equations. 1
 .4. The Fully Nonlinear CauchyKowaleskaya Theorem. 1
 .5. CauchyKowaleskaya with General Initial Surfaces. 1
 .6. The Symbol of a Differential Operator. 1
 .7. Holmgren's Uniqueness Theorem. 1
 .8. Fritz John's Global Holmgren Theorem. 1
 .9. Characteristics and Singular Solutions. 2 Some Harmonic Analysis. 2
 .1. The Schwartz Space $$\mathcal{J}({\mathbb{R}^d})$$. 2
 .2. The Fourier Transform on $$\mathcal{J}({\mathbb{R}^d})$$. 2
 .3. The Fourier Transform onLp$${\mathbb{R}^d}$$d):1 ?p?2. 2
 .4. Tempered Distributions. 2
 .5. Convolution in $$\mathcal{J}({\mathbb{R}^d})$$ and $$\mathcal{J}'({\mathbb{R}^d})$$. 2
 .6. L2Derivatives and Sobolev Spaces. 3 Solution of Initial Value Problems by Fourier Synthesis. 3
 .1. Introduction. 3
 .2. Schrodinger's Equation. 3
 .3. Solutions of Schrodinger's Equation with Data in $$\mathcal{J}({\mathbb{R}^d})$$. 3
 .4. Generalized Solutions of Schrodinger's Equation. 3
 .5. Alternate Characterizations of the Generalized Solution. 3
 .6. Fourier Synthesis for the Heat Equation. 3
 .7. Fourier Synthesis for the Wave Equation. 3
 .8. Fourier Synthesis for the CauchyRiemann Operator. 3
 .9. The Sideways Heat Equation and Null Solutions. 3
 .10. The HadamardPetrowsky Dichotomy. 3
 .11. Inhomogeneous Equations, Duhamel's Principle. 4 Propagators andxSpace Methods. 4
 .1. Introduction. 4
 .2. Solution Formulas in x Space. 4
 .3. Applications of the Heat Propagator. 4
 .4. Applications of the Schrodinger Propagator. 4
 .5. The Wave Equation Propagator ford = 1. 4
 .6. RotationInvariant Smooth Solutions of $${\square _{1 + 3}}\mu = 0$$. 4
 .7. The Wave Equation Propagator ford =3. 4
 .8. The Method of Descent. 4
 .9. Radiation Problems. 5 The Dirichlet Problem. 5
 .1. Introduction. 5
 .2. Dirichlet's Principle. 5
 .3. The Direct Method of the Calculus of Variations. 5
 .4. Variations on the Theme. 5.5.H1 the Dirichlet Boundary Condition. 5
 .6. The Fredholm Alternative. 5
 .7. Eigenfunctions and the Method of Separation of Variables. 5
 .8. Tangential Regularity for the Dirichlet Problem. 5
 .9. Standard Elliptic Regularity Theorems. 5
 .10. Maximum Principles from Potential Theory. 5
 .11. E. Hopf's Strong Maximum Principles. APPEND. A Crash Course in Distribution Theory. References.
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47. Partial differential equations [1997]
 Levine, Harold, 1922
 Providence, R.I. : American Mathematical Society : International Press, c1997.
 Description
 Book — xviii, 706 p. : ill. ; 26 cm.
 Summary

 Introduction Partial differentiation Solutions of PDE's and their specification PDE's and related arbitrary functions Particular solutions of PDE's Similarity solutions Correctly set problems Some preliminary aspects of linear first order PDE's First order PDE's, linear First order nonlinear PDE's Some technical problems and related PDE's First order PDE's, general theory First order PDE's with multiple independent variables Original detaials of the Fourier approach to boundary value problems Eigenfunctions and eigenvalues Eigenfunctions and eigenvalues, continued Nonorthogonal eigenfunctions Further example of Fourier style analysis Inhomogeneous problems Local heat sources An inhomogeneous configuration Other eigenfunction/eigenvalue problems Uniqueness of solutions Alternative representations of solutions Other differential equations and inferences therefrom Second order ODE's Boundary value problems and SturmLiouville theory Green's functions and boundary value problems Green's functions and generalizations PDE's, Green's functions, and integral equations Singular and infinite range problems Orthogonality and its ramifications Fourier expansions: Generalities Fourier expansions: Varied examples Fourier integrals and transforms Applications of Fourier transforms Legendre polynomials and related expansions Bessel functions and related expansions Hyperbolic equations Afterwords Bibliography Index.
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QA377 .L44 1997  Unknown 
 Bassanini, Piero.
 New York : Plenum Press, c1997.
 Description
 Book — ix, 439 p. : ill. ; 24 cm.
 Summary

This masterful text introduces firstyear graduate students to the basic ideas of the theory of partial differential equations in the context of the three fundamental equations of classical mathematical physics  the wave and heat equations and the Laplace equation. The authors avoid abstractions and succeed in demonstrating ideas by way of relatively simple, straightforward applications. Their book also deals with more advanced topics, including: the De GiorgiNashMoser theorem; nonlinear Dirichlet problems for elliptic equations; distributions and Sobolev spaces; and, hyperbolic conservation laws in one space variable.
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QA377 .B295 1997  Unknown 
49. Partial differential equations [1996]
 Taylor, Michael E., 1946
 New York : Springer, 1996.
 Description
 Book — 3 v.
 Summary

 13) Function space and operator theory for nonlinear analysis
 14) Nonlinear elliptic equations
 15) Nonlinear parabolic equations
 16) Nonlinear hyperbolic equations
 17) Euler and NavierStokes equations for incompressible fluids
 18) Einstein's equations.
 (source: Nielsen Book Data)
 Contents: Contents of Volumes I and III. Introduction. Pseudodifferential Operators. Spectral Theory. Scattering by Obstacles. Dirac Operators and Index Theory. Brownian Motion and Potential Theory. The PartialNeumann Problem. Connections and Curvature. Index.
 (source: Nielsen Book Data)
 Contents: Contents of Volumes II and III. Introduction. Basic Theory of ODE and Vector Fields. The Laplace Equation and Wave Equation. Fourier Analysis, Distributions, and ConstantCoefficient Linear PDE. Sobolev Spaces. Linear Elliptic Equations. Linear Evolution Equations. Appendix A: Outline of Functional Analysis. Appendix B: Manifolds, Vector Bundles, and Lie Groups. Index.
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(source: Nielsen Book Data)
This is the second of three volumes on partial differential equations. It builds upon the basic theory of linear PDE given in Volume 1, and pursues some more advanced topics in linear PDE. Analytical tools introduced in Volume 2 for these studies include pseudodifferential operators, the functional analysis of selfadjoint operators, and Wiener measure. There is also a development of basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
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This is the third of three volumes on partial differential equations. It is devoted to nonlinear PDE. There are treatments of a number of equations of classical continuum mechanics, including relativistic versions. There are also treatments of various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. Analytical tools introduced in this volume include the theory of L^p Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of CalderonZygmund theory and paradifferential operator calculus. The book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis.
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QA374 .T39 1996 V.1  Unknown 
QA374 .T39 1996 V.2  Unknown 
QA374 .T39 1996 V.3  Unknown 
50. Partial differential equations and applications : collected papers in honor of Carlo Pucci [1996]
 New York : Marcel Dekker, 1996.
 Description
 Book — 364 p.
 Summary

 Spatial decay estimates for an evolution equation
 on the range of Ural'tseva's axially symmetric operator in Sobolev spaces
 the use of a priori information in the solution of illposed problems
 allocation maps with general cost functions
 an elementary theorem in plane geometry and its multidimensional extension
 minimum problems for volumes of convex bodies
 on the continuous dependence of the solution of a linear parabolic partial differential equation on the boundary data and the solution at an interior spatial point
 decomposability of rectangular and triangular probability distributions
 nonlinear infinite networks with nonsymmetric resistances
 about a singular parabolic equation arising in thin film dynamics and in the Ricci flow for complete IR2
 alternatingdirection iteration for the pversion of the finite element method
 an integrodifferential analog of semilinear parabolic PDE's
 on solutions of mean curvature type inequalities
 an application of the calculus of variations to the study of optimal foraging
 a limit model of a soft thin joint
 projective invariants of complete intersections
 mhyperbolicity, evenness and normality
 an extended variational principle
 instability criteria for solutions of second order elliptic quasilinear differential equations
 maximum principles for difference operators
 a generic uniqueness result for the Stokes system and its control theoretical consequences
 on a Stefan problem in a concentrated capacity
 total total internal reflection
 the reflector problem for closed surfaces
 upper bounds for Eigenvalues of elliptic operators
 stability for abstract evolution equations
 new techniques in critical point theory
 detecting underground gas sources
 conservative operators
 on the regularization of the antenna synthesis problem
 the problem of packaging
 the first digit problem and scaleinvariance
 change of variable in the SLintegral
 the minimum energy configuration of a mixedmaterial column.
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QA371 .P36 1996  Available 
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