Qualitative properties for a Moore–Gibson–Thompson thermoelastic problem with heat radiation

In this work, we study some qualitative properties arising in the solution of a thermoelastic problem with heat radiation. The so-called Moore–Gibson–Thompson equation is used to model the heat conduction. By using the logarithmic convexity argument, the uniqueness and instability of solutions are p...

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Detalles Bibliográficos
Autores: Fernández García, José Ramón|||0000-0002-8533-1858, Quintanilla de Latorre, Ramón|||0000-0001-7059-7058
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/415037
Acceso en línea:https://hdl.handle.net/2117/415037
https://dx.doi.org/10.1007/s00707-024-04035-5
Access Level:acceso abierto
Palabra clave:Thermoelasticity
Termoelasticitat
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
Descripción
Sumario:In this work, we study some qualitative properties arising in the solution of a thermoelastic problem with heat radiation. The so-called Moore–Gibson–Thompson equation is used to model the heat conduction. By using the logarithmic convexity argument, the uniqueness and instability of solutions are proved without imposing any condition on the elasticity tensor. Then, the existence of solutions is obtained assuming that the elastic tensor is positive definite applying the theory of linear semigroups, and the exponential energy decay is shown in the one-dimensional case. Finally, we consider the one-dimensional quasi-static version and we assume that the elastic coefficient is negative. The existence and decay of solutions are proved, and a justification of the quasi-static approach is also provided.