\(n^2\) of dissipative couplings are sufficient to guarantee the exponential decay in elasticity
type: Item
instance of: scholarly article
title: \(n^2\) of dissipative couplings are sufficient to guarantee the exponential decay in elasticity
author: J. R. Fernández
author: Ramón Quintanilla
published in: Ricerche di Matematica
publication date: 2024-09-10T00:00:00Z
review text: In this paper, the authors first proved that, with \(n^2\) dissipation mechanisms and when the rank of the matrix defining the coupling coefficients is maximum, the solutions decay in an exponential way for every (bounded) geometry of the solid, where \(n\) is the dimension of the domain. Also, the authors provide an example when the matrix of coupling terms has rank 2 (in dimension 2) or rank 6 (in dimension 3) such that there are undamped isothermal mechanical oscillations.
reviewed by: R. Udhayakumar
Mathematics Subject Classification ID: 74H20
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74H40
Mathematics Subject Classification ID: 35Q74
zbMATH DE Number: 7909931
zbMATH Keywords: thermoelasticity
zbMATH Keywords: dissipation mechanism
zbMATH Keywords: energy decay
zbMATH Keywords: coupling coefficient matrix
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: undamped solution
MaRDI profile type: Publication
cites work: An inverse spectral theorem and its relation to the Pompeiu problem
cites work: Q4114384
cites work: Q5630603
cites work: Slow decay in linear thermoelasticity
cites work: Decay rates for the three-dimensional linear system of thermoelasticity
cites work: Q4239302
cites work: Q3335096
cites work: Q4024409
cites work: Stability in thermoelasticity of type III
cites work: Qualitative Aspects in Dual-Phase-Lag Thermoelasticity
cites work: Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity
DOI: 10.1007/S11587-022-00719-Z
description: scientific article; zbMATH DE number 7909931