Attractors of nonlinear elliptic equations with a small parameter
type: Item
instance of: scholarly article
title: Attractors of nonlinear elliptic equations with a small parameter
zbMATH Open document ID: 1013.35012
DOI: 10.1023/A:1012582031204
author: A. B. Shapoval
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The author studies the behavior of solutions to the equation \[ \varepsilon ^2u_{tt}(x,t)-2bu_t(x,t)+\triangle u(x,t)-f(u,t)=g(x,t),\quad x\in \Omega,\;t>0 \] satisfying data \(u=0\) on \(\partial \Omega , u(x,0)=u_0\) for \(\varepsilon \rightarrow 0.\) He proves upper semicontinuity of trajectory attractors in appropriate spaces.
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 1915935
zbMATH Keywords: trajectory attractor
zbMATH Keywords: small parameter
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: parabolic equation
zbMATH Keywords: upper semicontinuous sets
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: a:1012582031204
OpenAlex ID: W407306965
description: scientific article; zbMATH DE number 1915935