Exponential stability to a laminated beam in thermoelasticity of type III with delay

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III with delay term in the fourth equation. We first give the well-posedness of the system by using semigroup method and Lumer-Philips theorem. Then, by using the perturbed energy method and construct some Lyapunov functionals, we obtain the exponential decay result for the case of equal wave speeds.