Asymptotic behavior for a coupled Petrovsky and wave system with localized damping

In this paper we investigate asymptotic behavior for the solution of a coupled Petrovsky and wave system with locally distributed nonlinear interior damping. We establish a very general decay estimate for the energy by using an approach developed in Lasiecka and Tataru (1993) [23]. Using the energy decay formula, several explicit decay rate estimates can be obtained.