2016•IMA Journal of Mathematical Control and InformationRequires access

Controllability of the wave equation via multiplicative controls

Imad El Harraki, Ali Boutoulout

Abstract

In this paper, we study the controllability for the multidimensional wave equation. The first part deals with the linear wave equation with unbounded damping. Two multiplicative controls are constructed to conduct the solution of the system to a neighbourhood of the desired equilibrium state. The second part treats the controllability of the semi-linear wave equation. We show the approximate controllability for this problem, and we prove the exact controllability for the one-dimensional case using bilinear controls.

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Key concepts: Controllability, Multiplicative function, Wave equation, Mathematics, Neighbourhood (mathematics), Bilinear interpolation, Mathematical analysis, Riccati equation