Exponential stability of the semigroup associated with a thermoelastic system

Abstract

In this paper it is proved that the semigroup associated with the one-dimensional thermoelastic system with Dirichlet boundary conditions is an exponentially stable C 0 {C_0} -semigroup of contraction on the space H 0 1 × L 2 × L 2 H_0^1 \times {L^2} \times {L^2} . The technique of the proof is completely different from the usual energy method. It is shown that the exponential decay in D ( A ) D\left ( A \right ) recently obtained by Revira is a consequence of our main result. An important application of our main result to the Linear-Quadratic-Gaussian optimal control problem is also discussed.