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
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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