Time decay for several porous thermoviscoelastic systems of Moore–Gibson–Thompson type

Article type: Research Article

Authors: Bazarra, Noelia^a | Fernández, José R.^{a; *} | Magaña, Antonio^b | Quintanilla, Ramón^b

Affiliations: [a] Departamento de Matemática Aplicada I, Universidade de Vigo, 36310 Vigo, Spain. E-mails: nbazarra@uvigo.es, jose.fernandez@uvigo.es | [b] Departamento de Matemáticas, Universitat Politécnica de Catalunya, E.S.E.I.A.A.T., Colom 11, 08222 Terrassa, Barcelona, Spain. E-mails: antonio.magana@upc.edu, ramon.quintanilla@upc.edu

Correspondence: [*] Corresponding author: name surname, address. E-mail: jose.fernandez@uvigo.es.

Abstract: In this paper, we consider several problems arising in the theory of thermoelastic bodies with voids. Four particular cases are considered depending on the choice of the constitutive tensors, assuming different dissipation mechanisms determined by Moore–Gibson–Thompson-type viscosity. For all of them, the existence and uniqueness of solutions are shown by using semigroup arguments. The energy decay of the solutions is also analyzed for each case.

Keywords: Thermoviscoelasticity, existence and uniqueness, energy decay, dissipation mechanisms

DOI: 10.3233/ASY-211732

Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 339-359, 2022