Issue
EPL
Volume 77, Number 5, March 2007
Article Number 58006
Number of page(s) 5
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/77/58006
Published online 21 February 2007
EPL, 77 (2007) 58006
DOI: 10.1209/0295-5075/77/58006

Effect of memory kernels on the speed of reaction-diffusion fronts

V. Méndez1, S. Fedotov2 and W. Horsthemke3

1  Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona - E-08193 Bellaterra, Barcelona, Spain
2  School of Mathematics, The University of Manchester - Manchester M60 1DQ, UK
3  Department of Chemistry, Southern Methodist University - Dallas, TX 75275-0314, USA


received 2 August 2006; accepted in final form 18 January 2007; published March 2007
published online 21 February 2007

Abstract
We 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.

PACS
87.10.+e - Biological and medical physics: general theory and mathematical aspects.
05.40.-a - Fluctuation phenomena, random processes, noise and Brownian motion.
05.60.Cd - Classical transport.

© Europhysics Letters Association 2007