Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation
type: Item
instance of: scholarly article
title: Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation
zbMATH Open document ID: 1495.34080
author: Qian Yang
author: Mingkang Ni
published in: Science China. Mathematics
publication date: 2022-03-04T00:00:00Z
review text: In this paper, the authors extend and generalize the basic ideas in the case of problems with discontinuous time variables on the basis of contrast structure theory. They use the Butuzov method to construct a unified asymptotic expansion to describe the behavior of the solution in three different zones in the neighborhoods of boundary layers and internal layers. It is showed, that under certain assumptions, the scalar singularly perturbed boundary value problem \[ \mu^2\frac{d^2y}{dx^2}=f(y,x,\mu),\ 0 < x < 1,\ 0 < \mu \ll 1, \] \[ \frac{dy}{dx}(0,\mu) = 0, \ \frac{dy}{dx}(1,\mu) = 0, \] has a contrast structure solution with an internal layer in the neighborhood of the transition point \((x^*, d(x^*))\) on the discontinuous curve. The derived results have a potential to provide a useful tool for the applications and numerical methods of piecewise-smooth differential equations in many areas.
reviewed by: Robert Vrabel
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 7484064
zbMATH Keywords: reaction-diffusion equation
zbMATH Keywords: multizonal internal layer
zbMATH Keywords: asymptotic method
zbMATH Keywords: piecewise-smooth dynamical system
MaRDI profile type: Publication
full work available at URL: s11425-020-1856-4
OpenAlex ID: W3209315683
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DOI: 10.1007/S11425-020-1856-4
description: scientific article; zbMATH DE number 7484064