Growth and dispersal with inertia: hyperbolic reaction-transport systems.
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.
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.
Vicenç
V
Méndez
Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) Spain.
Daniel
D
Campos
Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA.
Werner
W
Horsthemke
D004058:Diffusion; D007700:Kinetics; D008962:Models, Theoretical