On the controllability of a Cubic Semi-Linear Wave Equation

A numerical method for a nonlinear control optimization of the open problem of the semi-linear wave equation stated by Jacques-Louis Lions (1928-2001) is depicted using the method of Glovinski-Lions-He. The goal of the numerical control depicted in this paper is to drive the state variable close to a given target function at finite time. Which is relevant because this equation without control decays or explodes. The results of the numerical experiments of a set of different target functions are satisfactory for the controllability and stability for an ad-hoc real control problem.