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
NASO, MARIA GRAZIA;
2002-01-01
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.File in questo prodotto:
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