A type III thermoelastic problem with two dissipative mechanisms

Abstract

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.

Keywords:

• Type III thermoelasticity
• dissipative mechanisms
• existence and uniqueness
• energy decay

2020 Mathematics Subject Classifications:

• 80-10
• 80M35
• 74B05
• 74F05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper is part of the project Qualitative and numerical analyses of problems in Thermomechanics (Ref. PID2023-146359NB-I00), which is currently under evaluation by the Spanish Ministry of Science, Innovation and Universities.