Clay Mathematics Proceedings
Volume: 17; 2013; 572 pp; Softcover
MSC: Primary 35; 58; 83; 42; 53;
Print ISBN: 978-0-8218-6861-4
Product Code: CMIP/17
List Price: $149.00
Individual Member Price: $119.20
Evolution EquationsShare this page
Edited by David Ellwood; Igor Rodnianski; Gigliola Staffilani; Jared Wunsch
A co-publication of the AMS and Clay Mathematics Institute
This volume is a collection of notes from
lectures given at the 2008 Clay Mathematics Institute Summer School,
held in Zürich, Switzerland. The lectures were designed for
graduate students and mathematicians within five years of the Ph.D.,
and the main focus of the program 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
Schrödinger equations) but also in the high energy or semi-classical
limits of elliptic problems.
The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting 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 Schrödinger 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 emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments.
Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Table of Contents
Table of Contents
Graduate students and research mathematicians interested in partial differentital equations and mathematical physics.