Abstract
We consider a nonlinear Klein-Gordon system posed in an inhomogeneous medium Ω with smooth boundary ∂Ω subject to a local damping distributed around a neighborhood ω of the boundary according to the Geometric Control Condition, where the nonlinearities have not growth restrictions. We show that the energy of the system goes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase-space.
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