Geodesic
Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a~solution of the boundary-value problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2009), pp. 76-83.

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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.
Keywords: optimal control, hyperbolic equation, penalty method, approximate solution. 
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S. Ya. Serovaǐskiǐ. Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a~solution of the boundary-value problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2009), pp. 76-83. http://geodesic.mathdoc.fr/item/IVM_2009_1_a3/

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