Abstract
We study a stabilization problem of a system coupled by a wave and a Euler–Bernoulli plate equation. Only one of the two equations is directly damped. Under some assumptions on the damping and the coupling terms, we prove that sufficiently smooth solutions of the system decay logarithmically without any geometric conditions on the damping domain. The proofs of these decay results rely on the interpolation inequalities for a coupled elliptic-parabolic system and the estimate of the resolvent operator for that system. The main tools to derive the desired interpolation inequalities are global Carleman estimates.
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