Rate of attraction for a semilinear thermoelastic system with variable coefficients
type: Item
instance of: scholarly article
title: Rate of attraction for a semilinear thermoelastic system with variable coefficients
zbMATH Open document ID: 1434.35215
author: Flank David Morais Bezerra
author: Milton L. Oliveira
author: Fágner D. Araruna
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2019-07-30T00:00:00Z
review text: In this paper the authors consider a family of one-dimensional semilinear thermoelastic problems. Thermal conductivity and elasticity depend on a parameter ``epsilon'' assumed small. Each one of the problems has its global attractor which depends on the parameter. The aim of the paper is to obtain an estimate of the distance between the attractor (depending on the parameter) and the limit corresponding to the case that the parameter vanishes. The authors prove that this distance can be estimated by means of the norm in the \(L^p\)-space (``\(p\)'' greater or equal to two) of the differences between the elasticities and the thermal conductivities. To obtain the results the authors study the resolvents of the linear operators to clarify the rate of convergence of the semigropus as well as the rate of convergence of the equilibria and of the linearizations.
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q79
Mathematics Subject Classification ID: 37L05
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 35B41
zbMATH DE Number: 7087137
zbMATH Keywords: thermoelastic system
zbMATH Keywords: global attractors
zbMATH Keywords: semigroups
zbMATH Keywords: rate of convergence
zbMATH Keywords: nonlinear dynamics
reviewed by: Ramón Quintanilla
MaRDI profile type: Publication
full work available at URL: dcdsb.2018316
OpenAlex ID: W2909466168
Wikidata QID: Q128422646
DOI: 10.3934/DCDSB.2018316
description: scientific article