Stability in thermoelastic diffusion theory with voids

Abstract

We analyse the longterm properties of a C ₀-semigroup describing the solutions to a linear evolution system of thermoelastic diffusion with porosity recently developed by Aouadi [M. Aouadi, A theory of thermoelastic diffusion materials with voids, Z. Angew. Math. Phys. 61 (2009), pp. 357–379]. It is shown that there exists coupling of elasticity with porosity, temperature and diffusion for isotropic bodies. Our main result is to prove the lack of exponential stability and that the time decay of the solutions can be controlled only by a polynomial. We conclude by showing the impossibility of location in time of the solutions.

Keywords:

• thermoelastic diffusion
• exponential stability
• polynomial stability
• impossibility of localization

AMS Subject Classifications::

• 35B35
• 74H55