Exponential stability of the semigroup associated with a thermoelastic system
In this paper it is proved that the semigroup associated with the onedimensional thermoelastic system with Dirichlet boundary conditions is an exponen12 2 tially stable C0-semigroup of contraction on the space H0 x L x L . The technique of the proof is completely different from the usual energy method. It is shown that the exponential decay in 3 (s/) recently obtained by Revira is a consequence of our main result. An important application of our main result to the Linear-QuadraticGaussian optimal control problem is also discussed.