**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2002; 311 pp; Softcover

MSC: Primary 34; 35; 37; 74;

Print ISBN: 978-0-8218-2625-6

Product Code: MMONO/209

Print ISBN: 978-0-8218-2625-6

Product Code: MMONO/209

List Price: $76.00

AMS Member Price: $60.80

MAA Member Price: $68.40

**Electronic ISBN: 978-1-4704-4634-5
Product Code: MMONO/209.E**

List Price: $76.00

AMS Member Price: $60.80

MAA Member Price: $68.40

# Far-from-Equilibrium Dynamics

Share this page
*Yasumasa Nishiura*

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.

#### Readership

Graduate students and research mathematicians interested in differential equations, dynamical systems, and ergodic theory.

#### Reviews & Endorsements

The book is well written, and the explanations are clear. … will be an excellent introduction to the field and a valuable resource for researchers in asymptotic analysis and pattern formation in PDEs.

-- Mathematical Reviews

A great resource for ideas and techniques in the analysis of pattern dynamics in continuous systems … accessible to a broad range of readers. Many examples illustrate and motivate the theory, summaries at the end of each chapter allow for reflection … several concise proofs are given. The rich bibliography makes in depth study possible … People interested in the theory of pattern formation should find this book instructive and inspiring reading.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Far-from-Equilibrium Dynamics

- Cover Cover11
- Title page v6
- Contents vii8
- Preface ix10
- Preface to the English edition xiii14
- Overview xv16
- Separation and unification of scales 122
- Amplitude equations 4162
- Marginal stability criterion and pattern selection 6990
- Pattern formation 111132
- Method of singular limit analysis 179200
- Transient dynamics 235256
- Future perspectives 285306
- Bibliography 291312
- Index 309330
- Back Cover Back Cover1336