Moore-Gibson-Thompson thermoelasticity with two temperatures

In this note we propose the Moore-Gibson-Thompson heat conduction equation with two temperatures and prove the well posedness and the exponential decay of the solutions under suitable conditions on the constitutive parameters. Later we consider the extension to the Moore-Gibson-Thompson thermoelasti...

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Bibliographic Details
Published inApplications in engineering science Vol. 1; p. 100006
Main Author Quintanilla, Ramón
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2020
Elsevier
Subjects
Exponential stability
Moore-Gibson-Thompson heat conduction
Polynomial decay
Slow decay
Two temperatures
Two temperatures
Slow decay
Exponential stability
Polynomial decay
Moore-Gibson-Thompson heat conduction
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Summary:In this note we propose the Moore-Gibson-Thompson heat conduction equation with two temperatures and prove the well posedness and the exponential decay of the solutions under suitable conditions on the constitutive parameters. Later we consider the extension to the Moore-Gibson-Thompson thermoelasticity with two temperatures and prove that we cannot expect for the exponential stability even in the one-dimensional case. This last result contrasts with the one obtained for the Moore-Gibson-Thompson thermoelasticity where the exponential decay was obtained. However we prove the polynomial decay of the solutions. The paper concludes by giving the main ideas to extend the theory for inhomogeneous and anisotropic materials.
ISSN:2666-4968
2666-4968
DOI:10.1016/j.apples.2020.100006