Abstract
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 reaction-diffusion 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.
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