Global attractors for quasilinear parabolic equations on unbounded thin domains
type: Item
instance of: scholarly article
title: Global attractors for quasilinear parabolic equations on unbounded thin domains
zbMATH Open document ID: 1379.35009
author: Ricardo P. Silva
published in: Monatshefte für Mathematik
publication date: 2016-08-01T00:00:00Z
review text: The author deals with the asymptotic behavior of a class of quasi-linear equations defined in an unbounded domain \(\Omega \subseteq \mathbb{R}^{n+1}\): \[ u_t -\Delta _p u + a(x,y) |u|^{p-2} u =f(u), \quad \text{in} \;\Omega, \] \[ {\frac {\partial u}{\partial n}} =0 \quad \text{ on } \;\partial \Omega, \] where \(\Delta_p =\operatorname{div} (|\nabla u|^{p-2} \nabla u)\) with \(2 < p < n\). Under certain conditions, the existence and upper semi-continuity of global attractors for the equations are proved when the \((n +1)\)-dimensional thin domain \(\Omega\) collapses to the entire space \(\mathbb{R}^n\).
reviewed by: Bixiang Wang
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B41
zbMATH DE Number: 6608243
zbMATH Keywords: thin domains
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: global attractors
MaRDI profile type: Publication
full work available at URL: s00605-016-0902-4
OpenAlex ID: W2310154942
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DOI: 10.1007/S00605-016-0902-4
description: scientific article; zbMATH DE number 6608243