Softcover ISBN:  9780821826256 
Product Code:  MMONO/209 
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eBook ISBN:  9781470446345 
Product Code:  MMONO/209.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
Softcover ISBN:  9780821826256 
eBook: ISBN:  9781470446345 
Product Code:  MMONO/209.B 
List Price:  $101.00 $76.50 
MAA Member Price:  $90.90 $68.85 
AMS Member Price:  $80.80 $61.20 
Softcover ISBN:  9780821826256 
Product Code:  MMONO/209 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $41.60 
eBook ISBN:  9781470446345 
Product Code:  MMONO/209.E 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
Softcover ISBN:  9780821826256 
eBook ISBN:  9781470446345 
Product Code:  MMONO/209.B 
List Price:  $101.00 $76.50 
MAA Member Price:  $90.90 $68.85 
AMS Member Price:  $80.80 $61.20 

Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 209; 2002; 311 ppMSC: Primary 34; 35; 37; 74;
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 spacetime 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.
ReadershipGraduate students and research mathematicians interested in differential equations, dynamical systems, and ergodic theory.

Table of Contents

Chapters

Separation and unification of scales

Amplitude equations

Marginal stability criterion and pattern selection

Pattern formation

Method of singular limit analysis

Transient dynamics

Future perspectives


Reviews

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


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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 spacetime 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.

Chapters

Separation and unification of scales

Amplitude equations

Marginal stability criterion and pattern selection

Pattern formation

Method of singular limit analysis

Transient dynamics

Future perspectives

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