Stability for coupled thermoelastic systems with viscoelastic damping and Wentzell boundary conditions

In this paper we study of a coupled thermoelastic system with viscoelastic damping term and Wentzell boundary conditions. We prove the existence as well as the stability of the energy associated to the problem. To prove the existence of solution we use semigroup theory and the stability is proved by multipliers techniques. The main goal is to bring the viscoelastic damping into the discussion concerning thermoelastic systems with Wentzell boundary conditions.