SUMMARYWe 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 sum of the ÿrst, second and third order energy associated with the system, we show that there exist positive constants C and satisfyingMoreover, the existence of absorbing sets is achieved in the non-homogeneous case.
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