Controllability of the semilinear wave equation governed by a multiplicative control

Mohamed Ouzahra

doi:10.3934/eect.2019039

Article Contents

2019, Volume 8, Issue 4: 669-686. Doi: 10.3934/eect.2019039

This issue Previous Article Next Article Simultaneous controllability of two vibrating strings with variable coefficients

Controllability of the semilinear wave equation governed by a multiplicative control

Mohamed Ouzahra^,

MASI Laboratory, Department of Mathematics & Informatics, ENS. University of Sidi Mohamed Ben Abdellah, Fes, P.O. Box 5206, Morocco

^* Corresponding author: M. Ouzahra
^* Corresponding author: M. Ouzahra

Dedicated to Professor Hammadi Bouslous on the occasion of his 65th birthday

Received: July 31, 2017

Revised: January 31, 2019

Early access: June 2019

Published: June 2019

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Abstract

In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the one dimensional version of the system at hand. The proof relies on linear semigroup theory and the results on the additive controllability of the semilinear wave equation. The approaches are constructive and provide explicit steering controls. Moreover, in the context of undamped wave equation, the exact controllability is established for a time which is uniform for all initial states.

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Mathematics Subject Classification: Primary: 93B05, 93C20; Secondary: 35L05.

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