Evolution equations : Clay Mathematics Institute Summer School, evolution equations, Eidgenössische Technische Hochschule, Zürich, Switzerland, June 23-July 18, 2008
- Corporate Author
- Clay Mathematics Institute. Summer School (2008 : Zürich, Switzerland)
- Providence, Rhode Island : American Mathematical Society ; [Cambridge, Mass.] : Clay Mathematics Institute, 
- Physical description
- viii, 572 pages ; 26 cm.
- Clay mathematics proceedings ; v. 17.
QC20.7 .E88 C53 2008
- Unknown QC20.7 .E88 C53 2008
- Includes bibliographical references.
- 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 many-body 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 semi-classical 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 mini-courses on the derivation of effective evolution equations from microscopic quantum dynamics, on wave maps with and without symmetries, on quantum N-body 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)
- Evolution equations.
- Wave equation.
- Partial differential equations -- Hyperbolic equations and systems -- Wave equation.
- Partial differential equations -- Hyperbolic equations and systems -- Nonlinear second-order hyperbolic equations.
- Partial differential equations -- Spectral theory and eigenvalue problems -- Scattering theory.
- Partial differential equations -- Equations of mathematical physics and other areas of application -- Time-dependent Schrödinger equations, Dirac equations.
- Partial differential equations -- Equations of mathematical physics and other areas of application -- NLS-like 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.
- Publication date
- David Ellwood, Igor Rodnianski, Gigliola Staffilani, Jared Wunsch, editors.
- Clay mathematics proceedings ; volume 17