Stabilization of Weakly Coupled Wave Equations Through a Density Term. (March 2021)

• Record Type: Journal Article
• Authors: Bel Hadj Salah, Monia
• Is Part Of: European journal of control. Volume 58(2021)
• Page Start: 315
• Page End: 326
• Publication Date: 2021-03
• Subjects: Coupled System -- Stabilization -- Spectral Theory -- Frequency approach; 35L05 -- 35B35 -- 35P20 -- 93D20 -- 65N25 -- 47D03; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2020.07.010
• Languages: English
• ISSNs: 0947-3580

Abstract

Abstract: We consider a system of two wave equations coupled through velocities with a boundary damping acting only in one equation. The main novelty in this paper is that we investigate stability properties of the system according to the strings densities. Indeed, our goal is to distribute mass along the damped string in such a way that the energy decays uniformly. Besides, the second string's density is fixed to one. We show that the dissipation given by the boundary condition of the damped string is sufficient to gain exponential stability if and only if the equations have the same density coefficients equal to one. Otherwise, we establish a polynomial energy decay rate of type 1 t . Our proofs rely on the frequency domain approach combined with a multiplier method.