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 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
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2. 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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3. 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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 Lorenzi, Luca, author.
 Second edition.  Boca Raton : CRC Press, [2017]
 Description
 Book — xl, 566 pages ; [ca. 2329] cm.
 Summary

 Markov semigroups in RN. Markov semigroups in unbounded open sets. A class of Markov semigroups in RN associated with degenerate elliptic operators. The nonautonomous setting. Appendices.
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6. Partial differential equations and applications : Collected Papers in Honor of Carlo Pucci [2017]
 Talenti, Giorgio, editor.
 First edition  Boca Raton, FL : CRC Press, 2017
 Description
 Book — 1 online resource : text file, PDF
 Summary

 Chapter Spatial Decay Estimates for an Evolution Equation / K. A. Ames Lawrence E. Payne
 chapter On the Range of Ural'tseva's Axially Symmetric Operator in Sobolev Spaces / Orazio Arena P. Manselli
 chapter The Use of "A Priori" Information in the Solution of IllPosed Problems / Mario Bertero
 chapter Allocation Maps with General Cost Functions / Luis A. Caffarelli
 chapter An Elementary Theorem in Plane Geometry and Its Multidimensional Extension / Francesco Calogero M. D. Kruskal
 chapter Minimum Problems for Volumes of Convex Bodies / Stefano Campi Andrea Colesanti Paolo Gronchi
 chapter 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 / John R. Cannon Salvadore PerezEsteva
 chapter Decomposability of Rectangular and Triangular Probability Distributions / Giorgio Dall' Aglio
 chapter Nonlinear Infinite Networks with Nonsymmetric Resistances / Leonede DeMichele Paolo M. Soardi
 chapter About a Singular Parabolic Equation Arising in Thin Film Dynamics and in the Ricci Flow for Complete IR2 / Emmanuele DiBenedetto David J. Diller
 chapter AlternatingDirection Iteration for the pVersion of the Finite Element Method / Jim Douglas
 chapter An Integrodifferential Analog of Semilinear Parabolic PDE's / Paul C. Fife
 chapter On Solutions of Mean Curvature Type Inequalities / Robert Finn
 chapter An Application of the Calculus of Variations to the Study of Optimal Foraging / Stefano Focardi Paolo Marcellini
 chapter A Limit Model of a Soft Thin Joint / Giuseppe Geymonat Françoise Krasucki
 chapter Projective Invariants of Complete Intersections / Francesco Gherardelli
 chapter MHyperbolicity, Evenness, and Normality / G. Gigante Giuseppe Tomassini
 chapter An Extended Variational Principle / Richard Jordan David Kinderlehrer
 chapter Instability Criteria for Solutions of Second Order Elliptic Quasilinear Differential Equations / B. Kawohl
 chapter Maximum Principles for Difference Operators / HungJu Kuo Neil S. Trudinger
 chapter A Generic Uniqueness Result for the Stokes System and Its Control Theoretical Consequences / JacquesLouis Lions Enrique Zuazua
 chapter On a Stefan Problem in a Concentrated Capacity / E. Magenes
 chapter Total Total Internal Reflection / Keith Miller
 chapter The Reflector Problem for Closed Surfaces / Vladimir Oliker
 chapter Upper Bounds for Eigenvalues of Elliptic Operators / Murray H. Protter
 chapter Stability for Abstract Evolution Equations / P. Pucci James Serrin
 chapter New Techniques in Critical Point Theory / Martin Schechter
 chapter Detecting Underground Gas Sources / Giorgio G. Talenti F. Tonani
 chapter Conservative Operators / Edoardo Vesentini
 chapter On the Regularization of the Antenna Synthesis Problem / Giovanni Alberto Viano
 chapter The Problem of Packaging / Piero Villaggio
 chapter The First Digit Problem and Scalelnvariance / Aljoša Volčič
 chapter Change of Variable in the SLIntegral / Rudolf Výborný
 chapter The Minimum Energy Configuration of a MixedMaterial Column / Hans F. Weinberger
 chapter Convergence of Regularized Solutions of Nonlinear IllPosed Problems with Monotone Operators / Fengshan Liu M. Zuhair Nashed
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 Salsa, S., author.
 Third edition.  Switzerland : Springer, [2016]
 Description
 Book — 1 online resource (xviii, 686 pages) : illustrations.
 Summary

 1 Introduction. 2 Diffusion. 3 The Laplace Equation. 4 Scalar Conservation Laws and First Order Equations. 5 Waves and vibrations. 6 Elements of Functional Analysis. 7 Distributions and Sobolev Spaces. 8 Variational formulation of elliptic problems. 9 Further Applications. 10 Weak Formulation of Evolution Problems. 11 Systems of Conservation Laws. 12 A Fourier Series. 13 B Measures and Integrals. 14 C Identities and Formulas.
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 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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11. 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 
12. 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 
 Basel : Birkhäuser, ©2011.
 Description
 Book — 1 online resource (vi, 367 pages).
 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.
15. 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.
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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.
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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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 Vol. 1: SpringerLink
 Vol. 2: SpringerLink
 Vol. 3: SpringerLink
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16. 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. (GSM/19.R).
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QA377 .E95 2010  Unknown 
17. 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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QA377 .A59 2009  Unknown 
 Milano : Springer, ©2009.
 Description
 Book — 1 online resource (xiii, 440 pages) : illustrations.
 Summary

Il testoè rivolto a studenti di Ingegneria, Matematica Applicata e Fisica edè disegnato per corsi alle fine del triennio o all'inizio del biennio magistrale. obiettivo didattico è duplice: da un lato presentare ed analizzare alcuni classici modelli differenziali della Meccanica dei Continui, completati da esercizi svolti e da simulazioni numeriche, illustrate usando il metodo delle differenze finite; dall'altro introdurre la formulazione variazionale dei più importanti problemi iniziali/al bordo, accompagnate da simulazioni numeriche effettuate utilizzando il metodo degli elementi finiti. In ultima analisi, il percorso didatticoè caratterizzato da una costante sinergia tra modelloteoriasimulazione numerica.
 Salsa, S.
 Milan : Springer, 2009.
 Description
 Book — 1 online resource (xv, 556 pages) : illustrations.
 Summary

 Diffusion. The Laplace Equation. Scalar Conservation Laws and First Order Equations. Waves and Vibrations. Elements of Functional Analysis. Distributions and Sobolev Spaces. Variational Formulation of Elliptic Problems. Weak Formulation of Evolution Problems.
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20. Principles of partial differential equations [2009]
 Komech, A. I.
 New York : SpringerVerlag, ©2009.
 Description
 Book — 1 online resource.
 Summary

 Hyperbolic equations. Method of characteristics
 The Fourier method
 Distributions and Green’s functions
 Fundamental solutions and Green’s functions in higher dimensions
 Erratum.
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