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On a Riemannian manifold of dimension $2 \leq d \leq 6$, with or withoutboundary, and whether bounded or unbounded, we consider a semilinear wave (orKlein-Gordon) equation with a subcritical nonlinearity, either defocusing orfocusing. We establish local controllability around a partially analyticsolution, under the geometric control condition. Specifically, some blow-upsolutions can be controlled. In the case of a Klein-Gordon equation on anon-trapping exterior domain, we prove the null-controllability of scatteringsolutions. The proof is based on local energy decay and global-in-timeStrichartz estimates. Some corollaries are given, including thenull-controllability of a solution starting near the ground state in certainfocusing cases, and exact controllability in certain defocusing cases.

Local controllability around a regular solution and null-controllability of scattering solutions for semilinear wave equations