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. 
@article{IVM_2009_1_a3,
     author = {S. Ya. Serovaǐskiǐ},
     title = {Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a~solution of the boundary-value problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--83},
     publisher = {mathdoc},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_1_a3/}
}
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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/