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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
1/2004

Traveling wave speeds of nonlocally perturbed reaction diffusion equations

Fathi Dkhil and Angela Stevens

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.

Received:
Jan 19, 2004
Published:
Jan 19, 2004
MSC Codes:
35B20, 35B50, 35C20, 35K55, 35K57, 35Q99, 45K05
Keywords:
nonlocal integro-differential equation, reaction-diffution equation, traveling wave speed

Related publications

inJournal
2006 Repository Open Access
Fathi Dkhil and Angela Stevens

Traveling wave speeds of nonlocally perturbed reaction-diffusion equations

In: Asymptotic analysis, 46 (2006) 1, pp. 81-91