Abstract
We consider the optimal control problem for a system governed by a nonlinear hyperbolic equation without any constraints on the parameter of nonlinearity. No uniqueness theorem is established for a solution to this problem. The control-state mapping of this system is not Gateaux differentiable. We study an approximate solution of the optimal control problem by means of the penalty method.
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Original Russian Text © S.Ya. Serovaiskii, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 1, pp. 76–83.
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Serovaiskii, S.Y. Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a solution of the boundary-value problem. Russ Math. 53, 64–70 (2009). https://doi.org/10.3103/S1066369X09010046
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DOI: https://doi.org/10.3103/S1066369X09010046