Asymptotic behavior of the wave equation under time-dependent fractional damping
In this paper, we analyze the stabilization of a wave equation subject to a fractional damping term that varies with time. We begin by proving the well-posedness of the system through the framework of semigroup theory for linear operators. Subsequently, we establish the strong stability of the solution. Furthermore, we derive general estimates for the energy decay rates. The methodology integrates tools from frequency domain analysis and multiplier techniques.
Authors
- Younes Bidi (ORCID: https://orcid.org/0000-0001-9881-6806)
- Abderrahmane Beniani (ORCID: https://orcid.org/0000-0002-5518-253X)
- Saleh Fahad Aljurbua (ORCID: https://orcid.org/0009-0004-1971-9418)
- Ahmed Bchatnia (ORCID: https://orcid.org/0000-0003-3795-5081)
Institutions
- Qassim University (SA)
- Université de ain Témouchent (DZ)
- Amar Telidji University of Laghouat (DZ)
- Tunis El Manar University (TN)
Publication Details
- Journal
- Journal of Inequalities and Applications
- Published
- 2026-01-05
- DOI
- https://doi.org/10.1186/s13660-025-03404-5
- Primary Topic
- Stability and Controllability of Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00