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Differential Equations

, Volume 54, Issue 5, pp 669–686 | Cite as

Solution of Contrast Structure Type for a Parabolic Reaction–Diffusion Problem in a Medium with Discontinuous Characteristics

  • A. O. Orlov
  • N. T. Levashova
  • N. N. Nefedov
Partial Differential Equations
  • 12 Downloads

Abstract

We consider a reaction–diffusion-type equation in a two-dimensional domain containing the interface between media with distinct characteristics along which the reactive term has a discontinuity of the first kind. We assume that the interface between the media, as well as the functions describing the reactions, periodically varies in time. We study the existence of a stable periodic solution of a problem with an internal layer. To prove the existence, stability, and local uniqueness of the solution, we use the asymptotic method of differential inequalities, which we generalized to a new class of problems with discontinuous nonlinearities.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • A. O. Orlov
    • 1
  • N. T. Levashova
    • 1
  • N. N. Nefedov
    • 1
  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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