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.
