Existence and Stability of a Front-Type Periodic Solution of a Two-Component System of Parabolic Equations


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Abstract

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.

About the authors

A. A. Melnikova

Faculty of Physics, Lomonosov Moscow State University

Author for correspondence.
Email: melnikova@physics.msu.ru
Russian Federation, Moscow, 119991

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