The Problem of the Optimal Control with a Lower Coefficient for Weakly Nonlinear Wave Equation in the Mixed Problem

Gunay Ismayilova

Abstract

In this paper, we consider the problem of determining the lowest coefficient of weakly nonlinear wave equation. The problem is reduced to the optimal control problem, in the new problem. In the this existence theorem of the optimal control and, the Fre ́echet differentiability of the functional is proved. Also the necessary condition of optimality is derived in view of variational inequality.

Keywords

coefficient, weakly nonlinear equation, optimal control,necessary condition

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