Existence and Asymptotic Representation of the Autowave Solution of a System of Equations

Abstract

A singularly perturbed parabolic system of nonlinear reaction–diffusion equations is studied. Systems of this class are used to simulate autowave processes in chemical kinetics, biophysics, and ecology. A detailed algorithm for constructing an asymptotic approximation of a travelling front solution is proposed. In addition, methods for constructing an upper and a lower solution based on the asymptotics are described. According to the method of differential inequalities, the existence of an upper and a lower solution guarantees the existence of a solution to the problem under consideration. These methods can be used for asymptotic analysis of model systems in applications. The results can also be used to develop and justify difference schemes for solving problems with moving fronts.