On a Periodic Inner Layer in the Reaction–Diffusion Problem with a Modular Cubic Source

Autor:	A. O. Orlov, N. N. Nefedov, E. I. Nikulin
Rok vydání:	2020
Předmět:	Lyapunov stability Computational Mathematics Nonlinear system Exponential stability business.industry Transition layer Mathematical analysis Reaction–diffusion system Layer (object-oriented design) Modular design business Differential inequalities Mathematics
Zdroj:	Computational Mathematics and Mathematical Physics. 60:1461-1479
ISSN:	1555-6662 0965-5425
DOI:	10.1134/s0965542520090134
Popis:	The article studies a singularly perturbed periodic problem for the parabolic reaction–diffusion equation in the case of a discontinuous source: a nonlinearity describing the reaction (interaction). The case of the existence of an inner transition layer under conditions of an unbalanced and a balanced reaction is considered. An asymptotic approximation is constructed, and the asymptotic Lyapunov stability of periodic solutions in each of the cases is investigated. To prove the existence of a solution and its asymptotic stability, the asymptotic method of differential inequalities is used. The theoretical result is illustrated by an example and numerical calculations.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ae0a97c1b9f528d8a071b513b36f89c6 https://doi.org/10.1134/s0965542520090134 Zobrazit plný text záznamu Full text from SpringerLink