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

摘要

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.