Logarithmic stabilization of the Euler-Bernoulli transmission plate equation with locally distributed Kelvin-Voigt damping

In this work we consider a transmission problem for a plate equation where one small part of the domain is made of a viscoelastic material with Kelvin-Voigt constitutive relation. We apply the general results due to Burq's [10] in the study of asymptotic behavior of solutions and prove that the semigroup associated to the system is logarithmically stable. The main ingredient of the proof is the Carleman estimates. The method consist to use Carleman estimates to obtain information on the resolvent for high frequency.