Stabilization of a Wave Equation with a General Internal Control
of Diffusive Type

Abdelkader Boudaoud; Abbes Benaissa$abbes@yahoo.com}

Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Stabilization of a Wave Equation with a General Internal Control of Diffusive Type

Discontinuity, Nonlinearity, and Complexity 12(4) (2023) 879--891 | DOI:10.5890/DNC.2023.12.012

Abdelkader Boudaoud, Abbes Benaissa$abbes@yahoo.com}

Laboratory of Analysis and Control of PDEs,Djillali Liabes University, P. O. Box 89, Sidi Bel Abbes 22000,

Algeria

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Abstract

In this paper, we study well-posedness and asymptotic stability of a wave equation with a general internal control of diffusive type. We prove that the system lacks exponential stability. Furthermore, we show an explicit and general decay rate result. The method is based on the frequency domain approach combined with multiplier technique.

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