Stabilization of the Weakly Coupled Wave-Plate System with One Internal Damping

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