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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 1, Pages 76–83 (Mi ivm1255)  
Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a solution of the boundary-value problem

S. Ya. Serovaĭskiĭ

Al-Farabi Kazakh National University
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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.
Keywords: optimal control, hyperbolic equation, penalty method, approximate solution.
Received: 26.01.2007
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, Volume 53, Issue 1, Pages 64–70
DOI: https://doi.org/10.3103/S1066369X09010046
Bibliographic databases:
UDC: 517.977
Language: Russian
Citation: S. Ya. Serovaǐskiǐ, “Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a solution of the boundary-value problem”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 1, 76–83; Russian Math. (Iz. VUZ), 53:1 (2009), 64–70
Citation in format AMSBIB
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\by S.~Ya.~Serova{\v\i}ski{\v\i}
\paper Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a~solution of the boundary-value problem
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 1
\pages 76--83
\mathnet{http://mi.mathnet.ru/ivm1255}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2530591}
\zmath{https://zbmath.org/?q=an:1180.49003}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 1
\pages 64--70
\crossref{https://doi.org/10.3103/S1066369X09010046}
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