Existence of Optimal Control for a Nonlinear Partial Differential Equation of Hyperbolic Type

Dieudonne Ampini, Mabonzo Vital Delmas

Abstract

In this paper, we prove the existence of an optimal control for a nonlinear hyperbolic problem, examined in [3]. An estimation is used which makes it possible to extract from a minimizable sequence of controls and from the sequence of corresponding solutions weakly convergent sub sequences. To prove the passage to the limit in a true equality for every element of the minimizable sequence, Lebesgue’s theorem on the passage to the limit under the integral sign and the theorem of immersion have been used.

Keywords

Optimal control; Hyperbolic equation; Functional.

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