Periodic Boundary Layer Solutions of a Reaction–Diffusion Problem with Singularly Perturbed Boundary Conditions of the Third Kindстатья
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Дата последнего поиска статьи во внешних источниках: 4 июня 2021 г.
Аннотация:We prove the existence and study the stability of time-periodic boundary layersolutions for a two-dimensional reaction–diffusion problem with a small parameter multiplying the parabolic operator for the case of singularly perturbed boundary conditions of the third kind. An asymptotic approximation to such solutions with respect to the small parameter is constructed. Conditions under which these solutions are Lyapunov asymptotically stable, as well as conditions under which such solutions are unstable, are obtained. For the proof, we used results based on applying the asymptotic method of differential inequalities and theKrein–Rutman theorem.