Thermoelasticity of Moore–Gibson–Thompson type with history dependence in the temperature

Article type: Research Article

Authors: Conti, Monica^a | Pata, Vittorino^a | Quintanilla, Ramon^{b; *}

Affiliations: [a] Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy. E-mails: monica.conti@polimi.it, vittorino.pata@polimi.it | [b] Departament de Matemàtiques, Universitat Politècnica de Catalunya, C. Colom 11, 08222 Terrassa, Barcelona, Spain. E-mail: ramon.quintanilla@upc.edu

Correspondence: [*] Corresponding author. E-mail: ramon.quintanilla@upc.edu.

Abstract: In this paper, we consider a thermoelastic model where heat conduction is described by the history dependent version of the Moore–Gibson–Thompson equation, arising via the introduction of a relaxation parameter in the Green-Naghdi type III theory. The well-posedness of the resulting integro-differential system is discussed. In the one-dimensional case, the exponential decay of the energy is proved.

Keywords: Moore–Gibson–Thompson equation, relaxation parameter, memory kernel, thermoelasticity, solution semigroup, exponential stability

DOI: 10.3233/ASY-191576

Journal: Asymptotic Analysis, vol. 120, no. 1-2, pp. 1-21, 2020