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Exact controllability for a semilinear wave equation with both interior and boundary controls. (English) Zbl 1098.35114

In this paper the author proved the existence of the exact controllability of a semilinear wave equation with both interior and boundary controls. In order to handle the nonlinear term, some compactness is needed. A different approach is taken in this paper, it is based on the theory of accretive operators. By assuming that \(f\) is accretive in the approximate space, the passage to the limit can be obtained and the target space is still the largest one, namely, \(L^2 (\Omega)\times H^{-1}(\Omega)\). The accretiveness hypothesis will replace the condition \(f'\) in \(L^\infty(\mathbb{R})\).

MSC:

35L70 Second-order nonlinear hyperbolic equations
93B05 Controllability
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