Decay estimates for a thermoelastic system in waveguides
type: Item
instance of: scholarly article
title: Decay estimates for a thermoelastic system in waveguides
zbMATH Open document ID: 1195.35055
author: Michael Dreher
author: Ya-Guang Wang
published in: Journal of Differential Equations
publication date: 2010-04-13T00:00:00Z
review text: The authors investigate the long time behaviour of solutions to the initial-boundary value problem of linear thermoelastic equations in \(\{(t,x): t>0\), \(x\in \Omega\}\) with \(\Omega=(0,1)\times \mathbb{R}^{n-1}\) being a so-called waveguide: \[ \begin{aligned} &u_{tt}-\mu\Delta u -(\mu+\lambda): \operatorname{grad\,div}u+\gamma_1:\operatorname{grad}\theta=f(t,x),\\ &\theta_t-\kappa\Delta \theta+\gamma_2: \operatorname{div}u_t=g(t,x),\quad (t,x)\in \mathbb{R}_+\times \Omega,\\ &(u,u_t,\theta)(0,x)=(u^0,u^1,\theta^0),\quad x\in \Omega,\\ &u_1(t,x)=\partial_\nu u_2(t,x)=\cdots=\partial_\nu u_n(t,x)=\partial_\nu \theta(t,x)=0,\quad (t,x)\in \mathbb{R}_+\times \Omega. \end{aligned} \] They prove decay estimates of the solutions which play a key role in showing the global existence of solutions.
reviewed by: Igor Bock
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35G15
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 74F05
zbMATH DE Number: 5692557
zbMATH Keywords: initial boundary value problems
zbMATH Keywords: parabolic-hyperbolic system
MaRDI profile type: Publication
full work available at URL: j.jde.2010.01.001
OpenAlex ID: W2130787679
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DOI: 10.1016/J.JDE.2010.01.001
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description: scientific article; zbMATH DE number 5692557