We show that the solution of a semilinear transmission problem between an elastic and a thermoelastic material, decays exponentially to zero. That is, denoting by $E(t)$ the first order energy associated to the system, we show that exist positive constants $C,$ and $\gamma$ satisfying: $$E(t)\leq CE(0)e^{-\gamma t}.$$ Moreover, the existence of absorbing sets and of an attractor is achieved in the non-homogeneous case.

### Asymptotic behaviour and exponential stability for a transmission problem in thermoelasticity

#### Abstract

We show that the solution of a semilinear transmission problem between an elastic and a thermoelastic material, decays exponentially to zero. That is, denoting by $E(t)$ the first order energy associated to the system, we show that exist positive constants $C,$ and $\gamma$ satisfying: $$E(t)\leq CE(0)e^{-\gamma t}.$$ Moreover, the existence of absorbing sets and of an attractor is achieved in the non-homogeneous case.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/699