This article is cited in 5 papers

Periodic Contrast Structures in the Reaction-Diffusion Problem with Fast Response and Weak Diffusion

N. N. Nefedov

Lomonosov Moscow State University

Abstract: In this paper, we study a new class of time-periodic solutions with interior transition layer of reaction-advection-diffusion equations in the case of a fast reaction and a small diffusion. We consider the case of discontinuous sources (i.e., the nonlinearity describing the interaction and reaction) for a certain value of the unknown function that arise in a number of relevant applications. An existence theorem is proved, asymptotic approximations are constructed, and the asymptotic Lyapunov stability of such solutions as solutions of the corresponding initial-boundary-value problems is established.

Keywords: reaction-advection-diffusion type equations, periodic parabolic boundary-value problems, singular perturbations, Burgers equations with modular advection, discontinuous sources, asymptotic method of differential inequalities, interior transition layer.

UDC: 517.95

Received: 15.05.2022

DOI: 10.4213/mzm13732

 English version: Mathematical Notes, 2022, 112:4, 588–597

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