Blowup for Nonlinear Hyperbolic Equations

Solutions to partial differential equations or systems often, over specific time periods, exhibit smooth behaviour. Given sufficient time, however, they almost invariably undergo a brutal change in behaviour, and this phenomenon has become known as "blowup". In this book, the author provides an overview of what is known about this situation and discusses many of the open problems concerning it. The book deals with classical solutions of global problems for hyperbolic equations or systems. The approach is based on the display and study of two local blowup mechanisms, which the author calls the "ordinary differential equation mechanism" and the "geometric blowup mechanism". It introduces, via energy methods, the concept of lifespan, related to the nonlinear propagation of regularity (from the past to the future). It addresses specifically the question of whether or not there will be blowup in a solution, and it classifies those methods used to give positive answers to the question. The material corresponds to a one semester course for students or researchers with a basic elementary knowledge of partial differential equations, especially of hyperbolic type including such topics as the Cauchy problem, wave operators, energy inequalities, finite speed of propagation, and symmetric systems. It contains a complete bibliography reflecting the high degree of activity among mathematicians interested in the problem.

ISBN 3764338105   DEWEY edition DC20 ISBN13 9783764338107 (What's this?)   Pages 128 Publisher Birkhauser Verlag AG   Volumes 001 Imprint Birkhauser Verlag AG   Published in Basel Format Hardback   Series editor Brezis, Haim (Universite et Marie Curie and Rutgers University, New Publication date 01 Mar 1995   Series title Progress in Nonlinear Differential Equations and Their Applications Library of Congress QA377   Height (mm) 240 DEWEY 515.353   Academic level Undergraduate, Postgraduate, Professional / Scholarly

Ch. I		The Two Basic Blowup Mechanisms		1
Ch. II		First Concepts on Global Cauchy Problems		25
Ch. III		Semilinear Wave Equations		40
Ch. IV		Quasilinear Systems in One Space Dimension		59
Ch. V		Nonlinear Geometrical Optics and Applications		82
		Bibliography		107
		Index		113

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