About this Title
Yasumasa Nishiura, Hokkaido University, Sapporo, Japan. Translated by Professor Kunimochi Sakamoto
Publication: Translations of Mathematical Monographs
Publication Year: 2002; Volume 209
ISBNs: 978-0-8218-2625-6 (print); 978-1-4704-4634-5 (online)
MathSciNet review: MR1903642
MSC: Primary 82C05; Secondary 34C60, 35B25, 35K55, 37N20, 82-02
This book is devoted to the study of evolution of nonequilibrium systems. Such a system usually consists of regions with different dominant scales, which coexist in the space-time where the system lives. In the case of high nonuniformity in special directions, one can see patterns separated by clearly distinguishable boundaries or interfaces.
The author considers several examples of nonequilibrium systems. One of the examples describes the invasion of the solid phase into the liquid phase during the crystallization process. Another example is the transition from oxidized to reduced states in certain chemical reactions. An easily understandable example of the transition in the temporal direction is a sound beat, and the author describes typical patterns associated with this phenomenon.
The main goal of the book is to present a mathematical approach to the study of highly nonuniform systems and to illustrate it with examples from physics and chemistry. The two main theories discussed are the theory of singular perturbations and the theory of dissipative systems. A set of carefully selected examples of physical and chemical systems nicely illustrates the general methods described in the book.
Graduate students and research mathematicians interested in differential equations, dynamical systems, and ergodic theory.
Table of Contents
- Separation and unification of scales
- Amplitude equations
- Marginal stability criterion and pattern selection
- Pattern formation
- Method of singular limit analysis
- Transient dynamics
- Future perspectives