Timoshenko system with a dual-phase-lag heat dissipation acting on the transversal displacement

In this paper, we prove the well-posedness and the exponential decay of the energy associated to the solution of a thermoelastic Timoshenko system with dual-phase-lag heat conduction. Using semigroup theory, we establish the existence and uniqueness of the solution. Then, by means of the multiplier method, we establish the exponential decay of the energy when the stability number vanishes. Finally, when the stability number is nonzero, we prove a polynomial decay result.