Asymptotics of periodic solutions of autonomous parabolic equations with small diffusion
type: Item
instance of: scholarly article
title: Asymptotics of periodic solutions of autonomous parabolic equations with small diffusion
zbMATH Open document ID: 0626.35045
DOI: 10.1007/BF00970006
published in: Siberian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Assume that the system \(\dot v=F(v,x)\) admits an exponentially orbitally stable periodic solution \(v_ 0(t,x)\) which depends smoothly on the parameter \(x\in [0,1]\). It is shown that close to \(v_ 0\) there exists an exponentially orbitally stable periodic solution of the system \[ u_ t=\mu u_{xx}+F(u,x),\quad 0<x<1, \] with Neumann or Dirichlet boundary conditions if \(\mu\) is small enough. The asymptotics (as \(\mu\to 0)\) of such solutions are derived.
reviewed by: Marek Fila
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 4017473
zbMATH Keywords: stable periodic solution
zbMATH Keywords: exponentially orbitally stable
zbMATH Keywords: Neumann
zbMATH Keywords: Dirichlet
author: S. A. Kashchenko
MaRDI profile type: Publication
cites work: Q3964370
cites work: Q4139051
cites work: Q3660139
cites work: Q3215647
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description: scientific article; zbMATH DE number 4017473