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In this paper we prove that the Ball-Marsden-Slemrod controllabilityobstruction also holds for nonlinear equations, with integrable bilinearcontrols. We first show an abstract result and then we apply it to nonlinearwave equations. The first application to the Sine-Gordon equation directlyfollows from the abstract result, and the second application concerns the cubicwave/Klein-Gordon equation and needs some additional work.

A topological obstruction to the controllability of nonlinear wave equations with bilinear control term