On the time decay in phase–lag thermoelasticity with two temperatures

Antonio Magaña; Alain Miranville; Ramón Quintanilla; Antonio Magaña; Alain Miranville; Ramón Quintanilla

doi:10.3934/era.2019007

Electronic Research Archive

2019, Volume 27, 7-19. doi: 10.3934/era.2019007

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On the time decay in phase–lag thermoelasticity with two temperatures

1.
Departament de Matemàtiques, Universitat Politècnica de Catalunya, 08222 Terrassa, Barcelona, Spain
2.
Laboratoire de Mathématiques et Applications, Université de Poitiers, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France

Received: 01 June 2019 Revised: 01 November 2019
Primary: 74F05, 74H40; Secondary: 74H20, 34B35, 35P20

The aim of this paper is to study the time decay of the solutions for two models of the one-dimensional phase-lag thermoelasticity with two temperatures. The first one is obtained when the heat flux vector and the inductive temperature are approximated by a second-order and first-order Taylor polynomial, respectively. In this case, the solutions decay in a slow way. The second model that we consider is obtained taking first-order Taylor approximations for the inductive thermal displacement, the inductive temperature and the heat flux. The decay is, therefore, of exponential type.
- Phase-lag thermoelasticity,
- exponential stability,
- slow decay,
- spectral analysis
Citation: Antonio Magaña, Alain Miranville, Ramón Quintanilla. On the time decay in phase–lag thermoelasticity with two temperatures[J]. Electronic Research Archive, 2019, 27: 7-19. doi: 10.3934/era.2019007

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Abstract

The aim of this paper is to study the time decay of the solutions for two models of the one-dimensional phase-lag thermoelasticity with two temperatures. The first one is obtained when the heat flux vector and the inductive temperature are approximated by a second-order and first-order Taylor polynomial, respectively. In this case, the solutions decay in a slow way. The second model that we consider is obtained taking first-order Taylor approximations for the inductive thermal displacement, the inductive temperature and the heat flux. The decay is, therefore, of exponential type.

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