We study the existence and uniqueness of traveling wave solutions for a class of two-component reaction-diffusion systems with one species being immobile. Such a system has a variety of applications in epidemiology, bio-reactor models, and isothermal autocatalytic chemical reaction systems. Our result not only generalizes earlier results of Ai and Huang (Proceedings of the Royal Society of Edinburgh 2005; 135A:663-675), but also establishes the existence and uniqueness of traveling wave solutions to the reactiondiffusion system for an isothermal autocatalytic chemical reaction of any order in which the autocatalyst is assumed to decay to the inert product at a rate of the same order.
ASJC Scopus subject areas
- Applied Mathematics