Propagating fronts in reaction–transport systems with memory

Abstract

In reaction-transport systems with non-standard diffusion, the memory of the transport causes a coupling of reactions and transport. We investigate the effect of this coupling for systems with Fisher-type kinetics and obtain a general analytical expression for the front speed. We apply our results to the specific case of subdiffusion.

Non-Markovian random walks and nonlinear reactions: Subdiffusion and propagating fronts

“…Therefore, the standard technique of FourierLaplace transforms can be employed to reduce the two balance equations (29) and (30) to a single equation for ρ (x, t). It turns out that this equation can be written as a phenomenological balance equation (28). So Eq.…”

“…This equation is different from the analogous one in [3,28]. The propagation rate v can be found from [23] …”

“…We apply these models to the problem of propagating fronts in reaction-transport systems with non-standard diffusion [23,24] (see also a recent review [25]). The theory of subdiffusive propagation of a front is presented in [3,11,[26][27][28][29][30], the superdiffusive propagation is studied in [31].…”

Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels

“…The figure reveals a rich class of sub-diffusive behaviours to process. Equation (45) implies in an extensive class of behaviour associated with rate r of added and removed walkers. The problem presented in this subsection makes clear that the non-Gaussian solutions found in Sections 3.1 and 3.2 have an important degree of applicability.…”

“…The Montroll-Weiss equation has several consequences in temporal memory and non-local behaviour in transport system in disordered medium and complex system [42][43][44]. The appropriate choice for waiting time distribution describes systems such as integration-differential equation with chemical interaction [24,45,46], anomalous diffusion in expanding media [30] and diffusion of single metal atoms on a graphene oxide support [47].…”