1 option
Traveling wave solutions of parabolic systems / Aizik I. Volpert, Vitaly A. Volpert, Vladimir A. Volpert.
- Format:
- Book
- Author/Creator:
- Volpert, Aizik, (Aizik Isaakovich), author.
- Series:
- Translations of mathematical monographs ; Volume 140.
- Translations of Mathematical Monographs ; Volume 140
- Standardized Title:
- Begushchie volny, opisyvaemye parabolicheskimi sistemami. English
- Language:
- English
- Subjects (All):
- Differential equations, Parabolic.
- Differential equations, Nonlinear.
- Chemical kinetics--Mathematical models.
- Physical Description:
- 1 online resource (xii, 448 pages).
- Place of Publication:
- Providence, R.I. : American Mathematical Society, [1994]
- Summary:
- 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.
- Notes:
- Includes bibliographical references (pages 427-448).
- Description based on print version record.
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.