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Research Article | Open Access

Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control

Ibtissam Issa1( ), Zayd Hajjej2
Dipartimento di Matematica, Università degli studi di Bari Aldo Moro, Via E. Orabona 4, Bari 70125, Italy
Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia
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Abstract

This paper explores the boundary stabilization of a degenerate wave equation in the non-divergence form, which includes a drift term and a singular potential term. Additionally, we introduce boundary fractional derivative damping at the endpoint where divergence is absent. Using semi-group theory and the multiplier method, we establish polynomial stability, with a decay rate depending upon the order of the fractional derivative.

Keywords

degenerate wave equationsingular potentialsdriftboundary stabilizationpolynomial decayfractional derivativenon-divergence form

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Electronic Research Archive
Volume 32 Issue 8,
August 2024
Pages 4926-4953
DOI: 10.3934/era.2024227

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Cite this article:
Issa I, Hajjej Z. Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control. Electronic Research Archive, 2024, 32(8): 4926-4953. https://doi.org/10.3934/era.2024227

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Received: 08 June 2024
Revised: 23 July 2024
Accepted: 08 August 2024
Published: 16 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)