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1997 Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
Xinfu Chen
Adv. Differential Equations 2(1): 125-160 (1997).

Abstract

The existence, uniqueness, and global exponential stability of traveling wave solutions of a class of nonlinear and nonlocal evolution equations are established. It is assumed that there are two stable equilibria so that a traveling wave is a solution that connects them. A basic assumption is the comparison principle: a smaller initial value produces a smaller solution. When applied to di↵erential equations or integro-di↵erential equations, the result recovers and/or complements a number of existing ones.

Citation

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Xinfu Chen. "Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations." Adv. Differential Equations 2 (1) 125 - 160, 1997.

Information

Published: 1997
First available in Project Euclid: 24 April 2013

zbMATH: 0934.35029
MathSciNet: MR1424765

Subjects:
Primary: 35A05, 35B05, 35B40, 35R99

Rights: Copyright © 1997 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.2 • No. 1 • 1997
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