zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Traveling wave solutions of parabolic systems. (English) Zbl 1001.35060
Translations of Mathematical Monographs. 140. Providence, RI: American Mathematical Society. xii, 448 p. (1994).
From the preface: The theory of traveling wave solutions of parabolic equations is one of the fast developing areas of modern mathematics. The history of this theory begins with the famous mathematical work by {\it A. N. Kolmogorov}, {\it I. G. Petrovskii} and {\it N. S. Piskunov} [Bull. Univ. État Moscou, Sér. Int., Sect. A: Math. et Mécan. 1, Fasc. 6, 1--25 (1937; Zbl 0018.32106)] and with works in chemical physics, the best known among them by Zel’dovich and Frank-Kamenetskii in combustion theory and by Semenov, who discovered branching chain flames. Traveling wave solutions are solutions of special type. They can be usually characterized as solutions invariant with respect to translation in space. The existence of traveling waves appears to be very common in nonlinear equations, and, in addition, they often determine the behavior of the solutions of Cauchy-type problems. From the physical point of view, traveling waves usually describe transition processes. Transition from one equilibrium to another is a typical case, although more complicated situations can arise. These transition processes usually forget their initial conditions and reflect the properties of the medium itself. Among the basic questions in the theory of traveling waves we mention the problem of wave existence, stability of waves with respect to small perturbations and global stability, bifurcations of waves, determination of wave speed, and systems of waves (or wave trains). The case of a scalar equation has been rather well studied, basically due to applicability of comparison theorems of a special kind for parabolic equations and of phase space analysis for the ordinary differential equations. For systems of equations, comparison theorems of this kind are, in general, not applicable, and the phase space analysis becomes much more complicated. This is why systems of equations are much less understood and require new approaches. In this book, some of these approaches are presented, together with more traditional approaches adapted for specific classes of systems of equations and for a more complete analysis of scalar equations. From the authors’ point of view, it is very important that these mathematical results find numerous applications, first and fore most in chemical kinetics and combustion. The authors understand that the theory of travelling waves is far from being complete and hope that this book will help in development. An excellent 20-page bibliography (over 500 entries) with a large number of Russian sources is also given. The book can be used by graduate students and researchers specializing in nonlinear differential equations, as well as by specialists in other areas (engineering, chemical physics, biology), where the theory of wave solutions of parabolic systems can be applied.

MSC:
35K57Reaction-diffusion equations
35-02Research monographs (partial differential equations)
80A30Chemical kinetics (thermodynamic aspects)
92E10Molecular structures
80A25Combustion, interior ballistics
35B40Asymptotic behavior of solutions of PDE
WorldCat.org
Full Text: Link