Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a solution of the boundary-value problem

Semen Ya. Serovaiskii

2009

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DOI 10.3103/s1066369x09010046
Data confidence 70 medium
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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.