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On an exact control problem for a semilinear wave equation with an unknown source. (English) Zbl 1188.93039

Summary: The exact controllability of a semilinear wave equation, with Dirichlet boundary control on a part of the boundary and an unknown source, is shown. The nonlinear term has at most a linear growth, the initial and target spaces are \(L^{2}(\Omega)\times H^{ - 1}(\Omega)\).

MSC:

93C20 Control/observation systems governed by partial differential equations
35L70 Second-order nonlinear hyperbolic equations
49L20 Dynamic programming in optimal control and differential games
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