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

Abdelkader Boudaoud, Abbes Benaissa

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.

Acknowledgments

The authors would like to thank very much the referees for their important remarks and suggestions which allow us to correct and improve this paper.

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