Potential well and exact boundary controllability for radial semilinear wave equations on Schwarzschild spacetime. (English) Zbl 1284.35254
Summary: We study the exact boundary controllability for the cubic focusing semilinear wave equation on Schwarzschild black hole background in radially symmetrical case. When the initial data and the final data are in the so called potential well, we find that the sufficient condition for the global existence is also sufficient to ensure the exact boundary controllability of the problem. Moreover, under the assumption of radial symmetry, our problem is changed to one space dimension case, and then the control time can be that of the linear wave equation.
MSC:
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 35L71 | Second-order semilinear hyperbolic equations |
| 93B05 | Controllability |
| 93C20 | Control/observation systems governed by partial differential equations |
Keywords:
semilinear wave equation; Schwarzschild spacetime; exact boundary controllability; potential well; cubic focusing nonlinearity; black hole backgroundReferences:
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