Traveling wave solutions of parabolic systems
Author(s)
Bibliographic Information
Traveling wave solutions of parabolic systems
（Translations of mathematical monographs, v. 140）
American Mathematical Society, c1994
- Other Title
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Бегущие волны, описываемые параболическими системами
Begushchie volny, opisyvaemye parabolicheskimi sistemami
Available at / 44 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:515/v9172070313316
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Note
Includes bibliography (p. 427-448)
Description and Table of Contents
Description
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.
Table of Contents
1: Part I. Stationary waves. 2: Scalar equation. 3: Leray-Schauder degree. 4: Existence of waves. 5: Structure of the spectrum. 6: Stability and approach to a wave. 7: Part II. Bifurcation of waves. 8: Bifurcation of nonstationary modes of wave propagation. 9: Mathematical proofs. 10: Part III. Waves in chemical kinetics and combustion. 11: Waves in chemical kinetics. 12: Combustion waves with complex kinetics. 13: Estimates and asymptotics of the speed of combustion waves. 14: Asymptotic and approximate analytical methods in combustion problems (supplement). 15: Bibliography
by "Nielsen BookData"
