Méndez Vicenç, Campos Daniel, Horsthemke Werner
Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) Spain and Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA.
Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042114. doi: 10.1103/PhysRevE.90.042114. Epub 2014 Oct 7.
We investigate the behavior of five hyperbolic reaction-diffusion equations most commonly employed to describe systems of interacting organisms or reacting particles where dispersal displays inertia. We first discuss the macroscopic or mesoscopic foundation, or lack thereof, of these reaction-transport equations. This is followed by an analysis of the temporal evolution of spatially uniform states. In particular, we determine the uniform steady states of the reaction-transport systems and their stability properties. We then address the spatiotemporal behavior of pure death processes. We end with a unified treatment of the front speed for hyperbolic reaction-diffusion equations with Kolmogorov-Petrosvskii-Piskunov kinetics. In particular, we obtain an exact expression for the front speed of a general class of reaction correlated random walk systems. Our results establish that three out of the five hyperbolic reaction-transport equations provide physically acceptable models of biological and chemical systems.
我们研究了五个最常用于描述相互作用的生物体或反应粒子系统的双曲反应扩散方程的行为，其中扩散表现出惯性。我们首先讨论这些反应输运方程的宏观或介观基础，或者缺乏这些基础的情况。接下来是对空间均匀状态的时间演化的分析。特别是，我们确定了反应输运系统的均匀稳态及其稳定性性质。然后我们研究纯死亡过程的时空行为。我们以对具有柯尔莫哥洛夫 - 彼得罗夫斯基 - 皮斯库诺夫动力学的双曲反应扩散方程的前沿速度的统一处理作为结束。特别是，我们得到了一类一般的反应相关随机游走系统的前沿速度的精确表达式。我们的结果表明，五个双曲反应输运方程中的三个为生物和化学系统提供了物理上可接受的模型。
