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

Ibtissam Issa; Zayd Hajjej; Ibtissam Issa; Zayd Hajjej

doi:10.3934/era.2024227

Electronic Research Archive

2024, Volume 32, Issue 8: 4926-4953. doi: 10.3934/era.2024227

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Research article

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

Ibtissam Issa ^{1
,
,},
Zayd Hajjej ²

1.
Dipartimento di Matematica, Università degli studi di Bari Aldo Moro, Via E. Orabona 4, Bari 70125, Italy
2.
Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 08 June 2024 Revised: 23 July 2024 Accepted: 08 August 2024 Published: 16 August 2024

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.
- degenerate wave equation,
- singular potentials,
- drift,
- boundary stabilization,
- polynomial decay,
- fractional derivative,
- non-divergence form
Citation: Ibtissam Issa, Zayd Hajjej. Stabilization for a degenerate wave equation with drift and potential term with boundary fractional derivative control[J]. Electronic Research Archive, 2024, 32(8): 4926-4953. doi: 10.3934/era.2024227

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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.

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