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Book reviews

Book reviews Acta Applicandae Mathematicae 3. (1985) 209 Joel Smoller: Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. Although applications are not the only source of good mathematical problems, the connection with natural sciences undoubtedly infuses a fresh spirit into mathematical research. The theory of partial differential equations is not an exception in this respect. In recent years, the main interest here has shifted from the field of linear equations to nonlinear problems. Surely, it is impossible to expect any interesting results if one does not restrict himself to a special class of nonlinear equations. Reaction-diffusion equations (RDE's) are a comparatively new class of such equations which have attracted keen interest in recent years. Usually, by RDE we mean equations and systems of the form OUk(t, x) (,) -- - D~uk + f~(x, ul,...,u,), t> 0, xeR r,k = L .... n. Ot Second-order linear operators L k of a general type with a nonnegative characteristic form may be involved in (,) instead of the operators D~A. One sometimes assumes that the coefficients of the operator Lk depend on u k. Such equations and systems have been considered since the 1930s by, in particular, R. Fisher and A. Kolmogorov, I. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

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References (6)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00580704
Publisher site
See Article on Publisher Site

Abstract

Acta Applicandae Mathematicae 3. (1985) 209 Joel Smoller: Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. Although applications are not the only source of good mathematical problems, the connection with natural sciences undoubtedly infuses a fresh spirit into mathematical research. The theory of partial differential equations is not an exception in this respect. In recent years, the main interest here has shifted from the field of linear equations to nonlinear problems. Surely, it is impossible to expect any interesting results if one does not restrict himself to a special class of nonlinear equations. Reaction-diffusion equations (RDE's) are a comparatively new class of such equations which have attracted keen interest in recent years. Usually, by RDE we mean equations and systems of the form OUk(t, x) (,) -- - D~uk + f~(x, ul,...,u,), t> 0, xeR r,k = L .... n. Ot Second-order linear operators L k of a general type with a nonnegative characteristic form may be involved in (,) instead of the operators D~A. One sometimes assumes that the coefficients of the operator Lk depend on u k. Such equations and systems have been considered since the 1930s by, in particular, R. Fisher and A. Kolmogorov, I.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Jun 9, 2004

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