Journal
MATHEMATICS AND MECHANICS OF SOLIDS
Volume 24, Issue 12, Pages 4020-4031Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1081286519862007
Keywords
Moore-Gibson-Thompson equation; relaxation parameter; thermoelasticity; existence; stability
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Funding
- Spanish Ministry of Economy and Competitiveness [MTM2016-74934-P]
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We consider a thermoelastic theory where the heat conduction is described by the Moore-Gibson-Thompson equation. In fact, this equation can be obtained after the introduction of a relaxation parameter in the Green-Naghdi type III model. We analyse the one- and three-dimensional cases. In three dimensions, we obtain the well-posedness and the stability of solutions. In one dimension, we obtain the exponential decay and the instability of the solutions depending on the conditions over the system of constitutive parameters. We also propose possible extensions for these theories.
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