Existence and Asymptotic Stability of Periodic Solutions of the Reaction–Diffusion Equations in the Case of a Rapid Reactionстатья
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Аннотация:A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal tran- sition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.