Abstract
In this paper, we study the exact boundarycontrollability for the cubic focusing semilinear wave equation onSchwarzschild black hole background in radially symmetrical case.When the initial data and the finaldata are in the so called potential well, we find that thesufficient condition for the global existence is also sufficient toensure the exact boundary controllability of the problem. Moreover,under the assumption of radial symmetry, our problem is changed toone space dimension case, and then the control time can be that of the linearwave equation.
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