J. Rauch: Hyperbolic Partial Differential Equations and Geometric Optics

摘要

(Graduate Studies in Mathematics, Vol. 133.) American Math. Society, Providence, Rhode Island, 2012, xix+363 S. ISBN 978-0-8218-721-8 H/b $ 64,-. This book is aimed at graduate students and young researchers and introduces the mathematical theory of geometric optics for linear and nonlinear (systems of) hyperbolic partial differential equations.The book fills a gap in the current literature since geometric optics is usually not treated (or only briefly mentioned) in most textbooks on partial differential equations.The author himself is a well known expert in this field and the present book has grown out of several graduate courses he has taught on this topic. The main physical motivation is the question of how one can deduce the classical theory of ray propagation from an underlying field theory based on hyperbolic differential equations, the main example being light rays, of course. Similar questions arise in fluid dynamics and also in quantum mechanics, where one aims to understand the emergence of classical particle dynamics within the solution of Schrodinger's equation.