OPTIMAL NECESSARY CONDITIONS OF COMMANDS FOR A NONLINEAR HYPERBOLIC PROBLEM WITH CONTINUOUS MEAN SQUARE POTENTIAL

This paper is devoted to the study of the optimal necessary conditions of a nonlinear hyperbolic equation with homogeneous Neumann condition, the initial conditions examined in [1]. For this, we constructed an integral functional depending on the solution of the problem and the commands (second member and initial conditions of the equation) whose differentiability has been shown in [2]. Then, we minimize the integral functional with equality and inequality type constraints which allowed us to obtain the optimal conditions of the first order from a conjugate problem obtained in [2] of which we generate the Hamiltonian form. Received: July 4, 2024Accepted: July 23, 2024