Traveling wave speeds of nonlocally perturbed reaction diffusion equations

Fathi Dkhil and Angela Stevens

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Submission date: 19. Jan. 2004
published in: Asymptotic analysis, 46 (2006) 1, p. 81-91 
Bibtex
MSC-Numbers: 35B20, 35B50, 35C20, 35K55, 35K57, 35Q99, 45K05
Keywords and phrases: nonlocal integro-differential equation, reaction-diffution equation, traveling wave speed

Abstract:
In this paper we consider a nonlocal integro-differential model as discussed by Bates et al. It is known that unique, stable traveling waves exist for the classical reaction-diffusion model as well as for the nonlocal model and for combinations of both for certain bistable nonlinearities. Here we are concerned with the traveling wave speed and how small perturbations with a nonlocal term affect the speed of the original reaction-diffusion problem. This is done by showing that an expansion for the wave speed of the perturbed problem exists and calculating the sign of the first order coefficient.