Structural stability results for the thermoelasticity of type III
type: Item
instance of: scholarly article
zbMATH Open document ID: 1307.35160
DOI: 10.4134/BKMS.2014.51.5.1269
author: Yan Liu
published in: Bulletin of the Korean Mathematical Society
publication date: 2014-10-17T00:00:00Z
full work available at URL: http://www.mathnet.or.kr/mathnet/kms_content.php
Mathematics Subject Classification ID: 35L53
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 6357689
zbMATH Keywords: convergence result
zbMATH Keywords: continuous dependence
MaRDI profile type: Publication
OpenAlex ID: W2313287128
title: Structural stability results for the thermoelasticity of type III
review text: The paper is concerned with the initial boundary value thermoelasticity problem NEWLINE\[NEWLINE\begin{aligned} &\rho \ddot u_i=\mu \Delta u_i+(\lambda+\mu)u_{j,ji}-\beta\dot\alpha_{,i}\;\text{in}\;\Omega ,\\ &c\ddot \alpha=-\beta \dot u_{i,i}+k\Delta \alpha+b \Delta \dot\alpha\;\text{in}\;\Omega ,\\ &u_i=\tilde{u}_i(\mathbf x),\;\alpha=\tilde\alpha(\mathbf x)\;\text{on}\;\partial\Omega,\\ &\alpha(\mathbf x,0=\alpha^0(\mathbf x),\;{u}_i(\mathbf x,0)={u}_i^0(\mathbf x),\;\dot{u}_i(\mathbf x,0)={\nu}_i^0(\mathbf x),\;\dot\alpha(\mathbf x,0)=\theta^0(\mathbf x). \end{aligned}NEWLINE\]NEWLINE The behavior of a solution \(\{u_i,\alpha\}\) as the specific heat \(c>0\) tends to zero is investigated. The energy method is the main tool used.
reviewed by: Igor Bock
description: scientific article; zbMATH DE number 6357689