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In this work, a type III thermoelastic problem is studied from the analytical point of view. Two dissipative mechanisms (the temperature and the mass diffusion) are also introduced and the material is assumed to be non-centrosymmetric, which will be needed in the analysis of the energy decay. It is remarkable that new coupling mechanisms appear. An existence and uniqueness result is proved by using the theory of linear semigroups. Then, assuming some specific conditions on the coupling tensors, the energy decay is shown to be exponential. Finally, some comments on the particular choices of the above tensors, and the resulting conditions for their coefficients, are provided.
Fernández et al. (2024) studied this question.