Well-posedness and exponential stability of Timoshenko system of second sound with time-varying delay and forcing terms

Abstract

As a continuity to the study by Ouchenane (Georgian Math J 21(4):475–489, 2014). We consider a nonlinear thermoelastic system of Timoshenko type with a time-varing delay and forcing term. We show the well-posedness of the system by using the semigroup theory, and we prove an exponential stability result under the usual assumption on the wave speed by the energy method.