Asymptotic Behaviour And Exponential Stability For A Thermoelastic Problem With Localized Damping

In this paper we consider a semi-linear transmission problem between an elastic and a thermoelastic material. We show that the solution of this problem exists and decays exponentially to zero. That is, denoting by ï¿¡(t) the sum of the first, second and third order energy associated with the system. We show that there exist positive constants C and 7 satisfyingMoreover, the existence of absorbing sets is achieved in the non-homogeneous case. In present paper is divided into four parts.In chapter 1, we give some functional setting and notation and a lemma and the existence and uniqueness of weak and strong solution and the regularity for this solution to system (l)-(9).In chapter 2, we derive the various energy estimates and we state the exponential decay of the solution.In chapter 3, we prove the existence of absorbing sets in the non-homogeneous case.