Evolution equations : Clay Mathematics Institute Summer School, evolution equations, Eidgenössische Technische Hochschule, Zürich, Switzerland, June 23July 18, 2008
 Corporate Author
 Clay Mathematics Institute. Summer School (2008 : Zürich, Switzerland)
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society ; [Cambridge, Mass.] : Clay Mathematics Institute, [2013]
 Physical description
 viii, 572 pages ; 26 cm.
 Series
 Clay mathematics proceedings ; v. 17.
Access
Available online

Stacks

Unknown
QC20.7 .E88 C53 2008

Unknown
QC20.7 .E88 C53 2008
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Contributors
 Contributor
 Ellwood, David, 1966 editor of compilation.
 Rodnianski, Igor, 1972 editor of compilation.
 Staffilani, Gigliola, 1966 editor of compilation.
 Wunsch, Jared, editor of compilation.
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 Table of Contents:* Microlocal analysis and evolution equations: Lecture notes from the 2008 CMI/ETH Summer School by J. Wunsch * Some global aspects of linear wave equations by D. Baskin and R. Mazzeo * Lectures on black holes and linear waves by M. Dafermos and I. Rodnianski * The theory of nonlinear Schrodinger equations by G. Staffilani * On the singularity formation for the nonlinear Schrodinger equation by P. Raphael * Nonlinear Schrodinger equations at critical regularity by R. Killip and M. Visan * Geometry and analysis in manybody scattering by A. Vasy * Wave maps with and without symmetries by M. Struwe * Derivation of effective evolution equations from microscopic quantum dynamics by B. Schlein.
 (source: Nielsen Book Data)
 Publisher's Summary
 This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zurich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the programme was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrodinger equations) but also in the high energy or semiclassical limits of elliptic problems. The three main courses presented focused mainly on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrodinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several minicourses on the derivation of effective evolution equations from microscopic quantum dynamics, on wave maps with and without symmetries, on quantum Nbody scattering, diffraction of waves, and symmetric spaces, and on nonlinear Schrodinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasises common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments.
(source: Nielsen Book Data)
Subjects
 Subject
 Evolution equations.
 Wave equation.
 Partial differential equations  Hyperbolic equations and systems  Wave equation.
 Partial differential equations  Hyperbolic equations and systems  Nonlinear secondorder hyperbolic equations.
 Partial differential equations  Spectral theory and eigenvalue problems  Scattering theory.
 Partial differential equations  Equations of mathematical physics and other areas of application  Timedependent Schrödinger equations, Dirac equations.
 Partial differential equations  Equations of mathematical physics and other areas of application  NLSlike equations (nonlinear Schro̲dinger)
 Partial differential equations  Equations of mathematical physics and other areas of application  Einstein equations.
 Global analysis, analysis on manifolds  Partial differential equations on manifolds; differential operators  Pseudodifferential and Fourier integral operators on manifolds.
 Global analysis, analysis on manifolds  Partial differential equations on manifolds; differential operators  Propagation of singularities; initial value problems.
 Global analysis, analysis on manifolds  Partial differential equations on manifolds; differential operators  Spectral problems; spectral geometry; scattering theory.
 Relativity and gravitational theory  General relativity  Black holes.
Bibliographic information
 Publication date
 2013
 Responsibility
 David Ellwood, Igor Rodnianski, Gigliola Staffilani, Jared Wunsch, editors.
 Series
 Clay mathematics proceedings ; volume 17
 ISBN
 9780821868614
 0821868616