RETARDATION EFFECTS IN A FINITE DIFFUSION-REACTION SYSTEM

Abstract

The reaction-diffusion process is generalized by including spatiotemporal delay effects. As a first example, we study the influence of a constant production term which is switched off after a finite time. In a second case, all diffusion-reaction processes within a distance R(t) = κtα around a certain spatial point are assumed to contribute to the instantaneous dynamics of the system. There occurs a competition between reaction-diffusion and the accumulation process which leads to a non-trivial stationary state. The evolving concentration profiles are calculated analytically for both a ballistic behavior with α = 1 and a diffusion-like transport with α = 1/2. Because the spatiotemporal delay breaks the reflection symmetry, the profiles reveal an anisotropic behavior. The exact solution in one dimension is supported by numerical simulations.