Translations of Mathematical Monographs Reprint
2 primary works
Book 140
Travelling Wave Solutions of Parabolic Systems
by Aizik I. Volpert, etc., Vitaly A. Volpert, and Vladimir A. Volpert
Published 8 December 1994
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 long-term 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 Leray-Schauder 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 reaction-diffusion systems can be reduced to so-called 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.
Mathematicians studying systems of partial differential equations, reaction-diffusion systems; physicists interested in autowave processes, dissipative structures; combustion scientists and chemists interested in mathematical issues of chemical kinetics.
Mathematicians studying systems of partial differential equations, reaction-diffusion systems; physicists interested in autowave processes, dissipative structures; combustion scientists and chemists interested in mathematical issues of chemical kinetics.
Book 163
Probability Theory
by A. Dorogovtsev, etc., D. S. Silvestrov, A. V. Skorokhod, and M. I. Yadrenko
Published 1 January 1997
This book of problems is intended for students in pure and applied mathematics. There are problems in traditional areas of probability theory and problems in the theory of stochastic processes, which has wide applications in the theory of automatic control, queuing and reliability theories, and in many other modern science and engineering fields. Answers to most of the problems are given, and the book provides hints and solutions for more complicated problems.