Advances in Differential Equations

Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations

Xinfu Chen

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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.

Article information

Source
Adv. Differential Equations, Volume 2, Number 1 (1997), 125-160.

Dates
First available in Project Euclid: 24 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366809230

Mathematical Reviews number (MathSciNet)
MR1424765

Zentralblatt MATH identifier
0934.35029

Subjects
Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B40: Asymptotic behavior of solutions 35A05 35R99: None of the above, but in this section

Citation

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


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