Advances in Differential Equations
- Adv. Differential Equations
- Volume 2, Number 1 (1997), 125-160.
Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
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.
Adv. Differential Equations Volume 2, Number 1 (1997), 125-160.
First available in Project Euclid: 24 April 2013
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Chen, Xinfu. Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations. Adv. Differential Equations 2 (1997), no. 1, 125--160. https://projecteuclid.org/euclid.ade/1366809230.