Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control
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 an...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-08-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024227 |
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| _version_ | 1832590808850628608 |
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| author | Ibtissam Issa Zayd Hajjej |
| author_facet | Ibtissam Issa Zayd Hajjej |
| author_sort | Ibtissam Issa |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-43b78995049d4005bcf07a8e9d6df38e |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-43b78995049d4005bcf07a8e9d6df38e2025-01-23T07:51:27ZengAIMS PressElectronic Research Archive2688-15942024-08-013284926495310.3934/era.2024227Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative controlIbtissam Issa0Zayd Hajjej1Dipartimento di Matematica, Università degli studi di Bari Aldo Moro, Via E. Orabona 4, Bari 70125, ItalyDepartment of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi ArabiaThis 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.https://www.aimspress.com/article/doi/10.3934/era.2024227degenerate wave equationsingular potentialsdriftboundary stabilizationpolynomial decayfractional derivativenon-divergence form |
| spellingShingle | Ibtissam Issa Zayd Hajjej Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control Electronic Research Archive degenerate wave equation singular potentials drift boundary stabilization polynomial decay fractional derivative non-divergence form |
| title | Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control |
| title_full | Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control |
| title_fullStr | Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control |
| title_full_unstemmed | Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control |
| title_short | Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control |
| title_sort | stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control |
| topic | degenerate wave equation singular potentials drift boundary stabilization polynomial decay fractional derivative non-divergence form |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024227 |
| work_keys_str_mv | AT ibtissamissa stabilizationforadegeneratewaveequationwithdriftandpotentialtermwithboundaryfractionalderivativecontrol AT zaydhajjej stabilizationforadegeneratewaveequationwithdriftandpotentialtermwithboundaryfractionalderivativecontrol |