Moore–Gibson–Thompson thermoelasticity

By Ramón Quintanilla. Mathematics and mechanics of solids, 2019

385 citations recorded by the source corpus.

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.

Subfields: Materials Chemistry, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/761060238ba62a8e00281237a7d5d1337d3b350c

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In Materials Chemistry

1. Ryo Ikehata
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In Mechanics of Materials

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Citations in the corpus

• The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case (2020, background): “Concerning some studies for the linear or nonlinear MGT equations, we refer interested readers to the related works [42, 54, 34, 20, 36, 35, 41, 33, 40, 49, 7, 16, 39, 17, 38, 48, 5, 1, 15, 6, 51, 47, 50, 11, 12, 4, 43, 44] and references therein.”