Evolution Equations

Evolution Equations

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This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in ZA¼rich, 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 SchrApdinger 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 SchrApdinger 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 SchrApdinger 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).Volume 17, 2013 . ... 1. Introduction The week-long minicourse on which this brief survey paper is based came after a vigorous, detailed ... Both lecture series took place at the Clay Mathematics Institute Summer School at ETH ZA¼rich in 2008. ... applied to solutions of the wave equation associated to a Laplace-type operator, can be used to obtain estimates for ... We give references for further reading interspersed inter alia, but do not make any claim to a comprehensive bibliography.

Title:Evolution Equations
Author: David Ellwood, Igor Rodnianski, Gigliola Staffilani, Jared Wunsch
Publisher:American Mathematical Soc. - 2013-06-26

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