V. Méndez et al 2007 EPL 77 58006 doi:10.1209/0295-5075/77/58006
V. Méndez1, S. Fedotov2 and W. Horsthemke3
Show affiliationsWe study the role of a memory kernel, in the constitutive equation for the particle flux, on the speed of propagating fronts in reaction-diffusion systems. We prove for general memory kernels the existence of propagating fronts with a speed bounded by the characteristics of the transport process, even in the fast-reaction limit. This upper bound depends only on the zero-delay value of the memory kernel. To illustrate our results, we consider examples of some functional forms for the memory kernel.
87.10.-e General theory and mathematical aspects
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
Issue 5 (March 2007)
Received 2 August 2006, in final form 18 January 2007
Published 21 February 2007
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