Stability of some thermoelastic systems with internal time-varying delay

In this paper we consider a thermoelastic type system with Cattaneo’s law and internal time-varying delay. Under suitable assumption on the weigh of delay, we prove the exponential stability of this system by using suitable energy functionals. More we show that the exponential stability of thermoelastic system with Cattaneo’s law implies a polynomial stability of the corresponding thermoelastic system with the Fourier’s law, where the result for the polynomial stability was proved recently by BorichevTomilov in [1].