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In this article we exploite the uniform decay for damped linear wave equationwith Zaremba boundary condition, obtained in a previous work, to treat the sameproblem in nonlinear context. We need a uniqueness assumption, usual for thistype of nonlinear problem. The result is deduced from an observation estimatefor nonlinear problem proved by a contradiction argument.

Semi-classical defect measure and internal stabilization for the semilinear wave equation subject to Zarembaboundary conditions