Asymptotic behaviour and exponential stability for a transmission problem in thermoelasticity



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 sum of the first, second and third order energy associated with the system, we show that there exist positive constants C and γsatisfying

ℰ(t) ⩽ Cℰ(0)e−γt

Moreover, the existence of absorbing sets is achieved in the non-homogeneous case. Copyright © 2002 John Wiley & Sons, Ltd.