Uniform stabilization for the coupled semi-linear wave and beam equations with distributed nonlinear feedback

In this paper, we consider a coupled semilinear wave and plate equations subject to an internal nonlinear damping locally distributed on an inhomogeneous medium Ω with smooth boundary ∂Ω. We are able to prove that the coupled system is well-posed in the sense of semigroups theory and more importantly, the associated energy decays uniformly to zero for all initial data of finite energy phase-space under reasonable conditions on the nonlinear functions involving the frictional dampings. Our approach consists to employ the observability inequality for the corresponding linear models.