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), as t -> +infinity. Our main result shows that the total energy of the system satisfies the following estimate: There exist a constant gamma = gamma (E (0)) > 0 such that E(t) <= 4E(0)exp(-gamma t) for all t >= 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. (c) 2005 Elsevier Ltd. All rights reserved.