Periodic Boundary Layer Solutions of a Reaction–Diffusion Problem with Singularly Perturbed Boundary Conditions of the Third Kind

Autor:	N. N. Nefedov, E. I. Nikulin
Rok vydání:	2020
Předmět:	Lyapunov function 0209 industrial biotechnology Partial differential equation General Mathematics Operator (physics) 010102 general mathematics Mathematical analysis 02 engineering and technology 01 natural sciences symbols.namesake Boundary layer 020901 industrial engineering & automation Stability theory Ordinary differential equation Reaction–diffusion system symbols Boundary value problem 0101 mathematics Analysis Mathematics
Zdroj:	Differential Equations. 56:1594-1603
ISSN:	1608-3083 0012-2661
Popis:	We prove the existence and study the stability of time-periodic boundary layer solutions for a two-dimensional reaction–diffusion problem with a small parameter multiplying the parabolic operator for the case of singularly perturbed boundary conditions of the third kind. An asymptotic approximation to such solutions with respect to the small parameter is constructed. Conditions under which these solutions are Lyapunov asymptotically stable, as well as conditions under which such solutions are unstable, are obtained. For the proof, we used results based on applying the asymptotic method of differential inequalities and the Krein–Rutman theorem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1216c79077d7e195bd774ba6d890a762 https://doi.org/10.1134/s00122661200120083 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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