

Preprint 1/2004
Traveling wave speeds of nonlocally perturbed reaction diffusion equations
Fathi Dkhil and Angela Stevens
Contact the author: Please use for correspondence this email.
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.