Translations of Mathematical Monographs 1994; 448 pp; softcover Volume: 140 Reprint/Revision History: reprinted 2000 ISBN10: 0821811436 ISBN13: 9780821811436 List Price: US$132 Member Price: US$105.60 Order Code: MMONO/140.S
 The theory of traveling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. The main part of the book contains original approaches developed by the authors. Among these are a description of the longterm behavior of the solutions by systems of waves; construction of rotations of vector fields for noncompact operators describing wave solutions; a proof of the existence of waves by the LeraySchauder method; local, global, and nonlinear stability analyses for some classes of systems; and a determination of the wave velocity by the minimax method and the method of successive approximations. The authors show that wide classes of reactiondiffusion systems can be reduced to socalled monotone and locally monotone systems. This fundamental result allows them to apply the theory to combustion and chemical kinetics. With introductory material accessible to nonmathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject. Readership Mathematicians studying systems of partial differential equations, reactiondiffusion systems; physicists interested in autowave processes, dissipative structures; combustion scientists and chemists interested in mathematical issues of chemical kinetics. Reviews "A wellwritten and welcome addition to the literature on this subject ... much of the text presents the results of papers that are only available in Russian and are not easily accessible to Western readers. Most of the book would be suitable for graduate students after a course in P.D.E., and the first part of the book contains an excellent introduction to the elementary aspects of the subject."  Bulletin of the AMS "A wellwritten book which covers in a very satisfying way a difficult subject matter, providing ... a wellbalanced interplay between theory and applications ..."  Mathematical Reviews Table of Contents Part I. Stationary waves  Scalar equation
 LeraySchauder degree
 Existence of waves
 Structure of the spectrum
 Stability and approach to a wave
Part II. Bifurcation of waves  Bifurcation of nonstationary modes of wave propagation
 Mathematical proofs
Part III. Waves in chemical kinetics and combustion  Waves in chemical kinetics
 Combustion waves with complex kinetics
 Estimates and asymptotics of the speed of combustion waves
 Asymptotic and approximate analytical methods in combustion problems (supplement)
 Bibliography
