Solutions for a hyperbolic diffusion equation with linear reaction terms

Abstract

Abstract General diffusion processes involve one or more diffusing species and are usually modelled by Fick’s law, which assumes infinite propagation velocity. In this article, searching for the effect of finite propagation speeds in a system with two reacting species, we investigate diffusing and reacting particles governed by a hyperbolic diffusion equation, that is, the Cattaneo equation, which describes a diffusion process with finite propagation velocity, in the presence of a constant external field and reaction terms. These reaction terms are linear and may be related to irreversible and reversible processes, including memory effects, depending on the choices of the reaction rates. We obtain exact solutions for the equilibrium concentrations and explore the rich variety of behaviours exhibited by the species involved in reaction processes. Our results may shine new light into systems with more than one kind of diffusing and reacting particles, as is the case in several industrial and biological process, when finite speeds and memory effects are involved.