Stability and energy decay rates in linear thermoelasticity*

摘要

We consider the initial-boundary value problem for a linear thermoelastic material characterized by Cattaneo-Maxwell's constitutive equation for the heat flux. We prove existence and uniqueness theorems for weak and strong solutions of the evolutive problem. Moreover, the dissipative effects of Cattaneo-Maxwell's relation allow us to prove, for the unidimensional model, the exponential decay of the energy associated to the system.