Existence and stability of a front-type periodic solution of a two-component system of parabolic equations

A periodic front-type solution of a singularly perturbed system of parabolic equations is considered. The system can be considered as a mathematical model describing a sharp change in the physical characteristics of spatially inhomogeneous media. Such models are used to describe processes in ecology, biophysics, chemical kinetics, combustion physics, and other fields. The existence of a front-type solution is proved, and the asymptotic stability of a periodic solution is established. An algorithm for constructing an asymptotic approximation of the solution is described.