On a periodic inner layer in the reaction-diffusion problem with a modular cubic sourceстатья
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Аннотация:—The article studies a singularly perturbed periodic problem for the parabolic reaction–dif-fusion equation in the case of a discontinuous source: a nonlinearity describing the reaction (interac- tion). The case of the existence of an inner transition layer under conditions of an unbalanced and a balanced reaction is considered. An asymptotic approximation is constructed, and the asymptotic Lyapunov stability of periodic solutions in each of the cases is investigated. To prove the existence of a solution and its asymptotic stability, the asymptotic method of differential inequalities is used. Thetheoretical result is illustrated by an example and numerical calculations.