Jem. Rivera et Md. Oliveira, EXPONENTIAL STABILITY FOR A CONTACT PROBLEM IN THERMOELASTICITY, IMA journal of applied mathematics, 58(1), 1997, pp. 71-82
We consider the unilateral problem for the thermoelastic equation and
we show that the solution decays exponentially to zero as time goes to
infinity; that is, denoting by E(t) the first-order energy of the sys
tem, we show that positive constants C and gamma exist which satisfy E
(t) less than or equal to CE(0)e(-gamma t).