Open AccessSolution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term
Author(s) -
Xiao Wu,
Mingkang Ni
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2020341
Subject(s) - mathematics , term (time) , mathematical analysis , type (biology) , diffusion , boundary value problem , contrast (vision) , dirichlet boundary condition , reaction–diffusion system , boundary (topology) , physics , thermodynamics , ecology , quantum mechanics , optics , biology
In this paper, we consider the Dirichlet boundary value problem for a singularly perturbed reaction-diffusion equation with discontinuous reactive term. We use the asymptotic analysis to construct the formal asymptotic approximation of the solution with internal and boundary layers. The internal layer is located in the vicinity of a curve of the discontinuous reactive term. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution and estimate the accuracy of its asymptotic approximation.