Traveling wave speeds of nonlocally perturbed reaction–diffusion equations

Article type: Research Article

Authors: Dkhil, F. | Stevens, A.

Affiliations: Département de Mathématiques, Institut Supérieur d'Informatique, Université Tunis El-Manar, 2 rue Abou Raihan Bayrouni, 2080 Ariana, Tunisie E-mail: fathi.dkhil@isi.rnu.tn | Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany E-mail: stevens@mis.mpg.de

Abstract: In this paper we consider a nonlocal integro-differential model as it was discussed by Bates and Chen [Electron. J. Differential Equations 1999(26) (1999), 1–19]. 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. We show that an expansion for the wave speed of the perturbed problem exists and calculate the sign of the first-order coefficient.

Keywords: nonlocal integro-differential equation, reaction–diffusion equation, traveling wave speed

Journal: Asymptotic Analysis, vol. 46, no. 1, pp. 81-91, 2006