Energy decay rates for the Timoshenko system of thermoelastic plates

We consider a model describing nonlinear dynamical motions of an unbounded thermoelastic plate. We prove the well-posedness of the above system and analyse the behaviour of the total energy E(t)E(t), as t→+∞t→+∞. Our main result shows that the total energy of the system satisfies the following estimate: There exist a constant γ=γ(E(0))>0γ=γ(E(0))>0 such thatE(t)⩽4E(0)exp(-γt)forallt⩾0.The result is proved by constructing a Lyapunov function which is a suitable perturbation of the energy and satisfies a differential inequality leading to the desired decay estimate.