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On Unstable Solutions with a Nonmonotone Boundary Layer in a Two-Dimensional Reaction-Diffusion Problem

Authors
  • Nefedov, N. N.1
  • Nikulin, E. I.1
  • 1 Lomonosov Moscow State University, Moscow, 119991, Russia , Moscow (Russia)
Type
Published Article
Journal
Mathematical Notes
Publisher
Pleiades Publishing
Publication Date
Nov 01, 2021
Volume
110
Issue
5-6
Pages
922–931
Identifiers
DOI: 10.1134/S0001434621110286
Source
Springer Nature
Keywords
Disciplines
  • article
License
Yellow

Abstract

Abstract The paper deals with the study of time-periodic solutions of boundary layer type for a two-dimensional reaction-diffusion problem with a small parameter at the parabolic operator in the case of singularly perturbed boundary conditions of the second kind. The asymptotic approximation with respect to the small parameter for solutions with a nonmonotone boundary layer is constructed. It is shown that all such solutions are unstable. The proof of the instability of the solutions is based on the construction of an unordered pair of upper and lower solutions and on the application of a corollary of the Krein–Rutman theorem.

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