Asymptotic Behavior in Linear Thermoelasticity

This paper studies a linear thermoelastic material which exhibits a constitutive equation for heat flux with memory. An approximated theory of thermodynamics is developed for this model and a maximal pseudo free energy is explicitly constructed in the frequency domain. This thermodynamic potential is used to prove stability and domain of dependence results. Moreover, by the thermodynamic restrictions on the heat flux kernel, existence, uniqueness, and asymptotic behavior theorems are proved for the unidimensional model.