General boundary stabilization of memory-type thermoelasticity with second sound
type: Item
instance of: scholarly article
title: General boundary stabilization of memory-type thermoelasticity with second sound
zbMATH Open document ID: 1263.35039
DOI: 10.4171/ZAA/1468
author: Aisha Al-Shehri
author: Salim A. Messaoudi
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2012-12-06T00:00:00Z
review text: The authors study the time-asymptotic behavior of solutions to an \(n\)-dimensional system of visco-thermoelasticity with second sound in a bounded domain. For the Dirichlet problem, the exponential decay of solutions was established in [\textit{R. Racke}, Q. Appl. Math. 61, No. 2, 315--328 (2003; Zbl 1030.74018)] provided that \(\text{rot}\,u=\text{rot}\,q=0\). As a consequence, the radially symmetric solution to the Dirichlet problem decays exponentially. In this paper, the authors consider the case that a viscoelastic dissipation of memory type is acting on a part of the boundary. Exploiting the boundary dissipation and using careful energy estimates to construct an appropriate Lyapunov functional, the authors prove a general uniform stability (including polynomial decay) of the solution energy under suitable conditions on the boundary and the kernels of general-type decay.
reviewed by: Song Jiang
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35L53
Mathematics Subject Classification ID: 74D05
Mathematics Subject Classification ID: 74F05
zbMATH DE Number: 6113166
zbMATH Keywords: general decay
zbMATH Keywords: polynomial decay
zbMATH Keywords: relaxation function
zbMATH Keywords: Lyapunov functional
MaRDI profile type: Publication
cites work: Exponential decay of non-linear wave equation with a viscoelastic boundary condition
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cites work: Q4386841
cites work: General decay rates of solutions to a nonlinear wave equation with boundary condition of memory type.
cites work: Stability of equilibrium for a nonlinear hyperbolic system describing heat propagation by second sound in solids
full work available at URL: https://doi.org/10.4171/zaa/1468
OpenAlex ID: W1984724975
description: scientific article; zbMATH DE number 6113166