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.

一般的扩散过程涉及一个或多个扩散物质，通常通过菲克定律建模，该定律假定传播速度为无限。在本文中，为了寻找具有两个反应物种的系统中有限传播速度的影响，我们研究了由双曲线扩散方程（即Cattaneo方程）控制的粒子的扩散和反应粒子，该方程描述了具有有限传播速度的扩散过程，在恒定的外部场和反应条件下 这些反应项是线性的，并且取决于反应速率的选择，可能与不可逆和可逆过程有关，包括记忆效应。我们获得了平衡浓度的精确解，并探索了反应过程中涉及的物种所表现出的多种行为。