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The Existence and Stability of Periodic Solutions with a Boundary Layer in a Two-Dimensional Reaction-Diffusion Problem in the Case of Singularly Perturbed Boundary Conditions of the Second Kind
Moscow University Physics Bulletin ( IF 0.4 ) Pub Date : 2020-08-27 , DOI: 10.3103/s0027134920020083 N. N. Nefedov , E. I. Nikulin
中文翻译:
第二类边界条件奇摄动的二维反应扩散问题边界层周期解的存在性和稳定性
更新日期:2020-08-27
Moscow University Physics Bulletin ( IF 0.4 ) Pub Date : 2020-08-27 , DOI: 10.3103/s0027134920020083 N. N. Nefedov , E. I. Nikulin
Abstract
The existence of time-periodic solutions of the boundary-layer type to a two-dimensional reaction–diffusion problem with a small-parameter coefficient of a parabolic operator is proved in the case of singularly perturbed boundary conditions of the second kind. An asymptotic approximation with respect to the small parameter is constructed for these solutions. The set of boundary conditions for which these solutions exist is studied and the local uniqueness and asymptotic Lyapunov stability are established for them. It is shown that, unlike the analogous Dirichlet problem, for which such a solution is unique, there can be several solutions of this kind for the problem under consideration, each of which has its domains of stability and local uniqueness. To prove these facts, results based on the asymptotic principle of differential inequalities are used.Keywords: , , , , , , .中文翻译:
第二类边界条件奇摄动的二维反应扩散问题边界层周期解的存在性和稳定性