Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya. Departament de Matemàtiques
Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada
Universitat Politècnica de Catalunya. GRTJ - Grup de Recerca en Teoria de Jocs
2019-09-01
In this paper we consider the one-dimensional version of thermoelasticity with two porous structures and porous dissipation on one or both of them. We first give an existence and uniqueness result by means of semigroup theory. Exponential decay of the solutions is obtained when porous dissipation is assumed for each porous structure. Later, we consider dissipation only on one of the porous structures and we prove that, under appropriate conditions on the coefficients, there exists undamped solutions. Therefore, asymptotic stability cannot be expected in general. However, we are able to give suitable sufficient conditions for the constitutive coefficients to guarantee the exponential decay of the solutions.
Peer Reviewed
Postprint (author's final draft)
Article
English
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències; Thermoelasticity; Porous materials -- Thermal properties; Decay estimate; Exponential decay; Existence and uniqueness of solutions; semigroup argument; Thermoelasticity with two porosities; Materials porosos -- Propietats tèrmiques; Termoelasticitat; Classificació AMS::74 Mechanics of deformable solids; Classificació AMS::35 Partial differential equations
http://journals.sagepub.com/doi/abs/10.1177/1081286518783219
info:eu-repo/grantAgreement/MINECO/1PE/MTM2016-74934-P
info:eu-repo/grantAgreement/MINECO//MTM2013-42004-P/ES/ANALISIS MATEMATICO DE LAS ECUACIONES EN DERIVADAS PARCIALES DE LA TERMOMECANICA/
Open Access
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