Well-posedness and stability results in a Timoshenko-type system of thermoelasticity of type III with delay
type: Item
instance of: scholarly article
title: Well-posedness and stability results in a Timoshenko-type system of thermoelasticity of type III with delay
zbMATH Open document ID: 1348.35031
author: Muhammad Kafini
author: Muhammad I. Mustafa
author: Salim A. Messaoudi
author: Tijani A. Apalara
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2015-09-03T00:00:00Z
review text: The authors consider the following Timoshenko system of thermoelasticity of type III with discrete delay (for \(x \in (0,1)\) and \(t \geqslant 0\)) \[ \begin{cases}\rho_{1}\phi_{tt}-K(\phi_{x}+\psi)_{x}+\mu_{1}\phi_{t}(x,t)+\mu_{2}\phi _{t}(x,t-\tau)=0,\\ \rho_{2}\psi_{tt}-b\psi_{xx}+K(\phi_{x}+\psi)+\beta\theta_{tx}=0,\\ \rho_{3}\theta_{tt}-\delta\theta_{xx}+\gamma\psi_{tx}-k\theta_{txx} =0. \end{cases} \] These equations are complemented with initial data and history \(\phi _{t}(x,t-\tau)=f_{0}(x,t-\tau)\), \(t\in(0,\tau)\) together with Dirichlet boundary conditions for the first two components and Neumann boundary conditions for the third component. After proving the well-posedness in an appropriate space, the authors determined mainly two types of decay of the energy. Namely, an exponential decay in case of equal wave speeds and a polynomial decay in case of nonequal wave speeds. This is established in spite of the presence of the delay in the system.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L53
Mathematics Subject Classification ID: 74H40
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 6478439
zbMATH Keywords: uniform decay
zbMATH Keywords: delay
zbMATH Keywords: one space dimension
reviewed by: N.-E. Tatar
MaRDI profile type: Publication
full work available at URL: s00033-014-0475-9
OpenAlex ID: W2093602103
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DOI: 10.1007/S00033-014-0475-9
description: scientific article; zbMATH DE number 6478439