Effect of memory kernels on the speed of reaction-diffusion frontsV. 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
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.
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