Energy decay for a degeneratewave equation under fractional derivative controls

Benaissa, Abbès; Aichi, Chahira

doi:10.2298/fil1817045b

Cited by 6 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 5.4. We can extend the results of this paper to more general measure density (see [10]) instead of (5). Indeed, let us suppose that ν is an even nonnegative measurable function such that…”

mentioning

confidence: 86%

“…They proved an optimal polynomial decay rate. It is proved that the presence of feedback of fractional time derivative type and located at a nondegenerate point x = 1 has no effect on the stabilisation results in [5].…”

Section: (P)mentioning

confidence: 99%

“…• The frequency method based on multiplier techniques used in [5] and the enegy method based on multiplier techniques used in [16] do not seem to be work in the case of a feedback located at a degenerate point x = 0.…”

Section: (P)mentioning

confidence: 99%

See 2 more Smart Citations

Decay estimates for a degenerate wave equation with a dynamic fractional feedback acting on the degenerate boundary

Chouaou

Aichi

Benaissa

2021

Filomat

Self Cite

View full text Add to dashboard Cite

In this paper, we consider a one-dimensional weakly degenerate wave equation with a dynamic nonlocal boundary feedback of fractional type acting at a degenerate point. First We show well-posedness by using the semigroup theory. Next, we show that our system is not uniformly stable by spectral analysis. Hence, we look for a polynomial decay rate for a smooth initial data by using a result due Borichev and Tomilov which reduces the problem of estimating the rate of energy decay to finding a growth bound for the resolvent of the generator associated with the semigroup. This analysis proves that the degeneracy affect the energy decay rates.

show abstract

mentioning

confidence: 86%

Section: (P)mentioning

confidence: 99%

See 1 more Smart Citation

Decay estimates for a degenerate wave equation with a dynamic fractional feedback acting on the degenerate boundary

Chouaou

Aichi

Benaissa

2021

Filomat

Self Cite

View full text Add to dashboard Cite

show abstract

The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect

Akil,

Fragnelli,

Issa

2024

Mathematische Nachrichten

View full text Add to dashboard Cite

In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type . Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied.

show abstract

On the Stability of a Degenerate Wave Equation Under Fractional Feedbacks Acting on the Degenerate Boundary

2022

View full text Add to dashboard Cite

Energy decay for a degeneratewave equation under fractional derivative controls

Cited by 6 publications

References 15 publications

Decay estimates for a degenerate wave equation with a dynamic fractional feedback acting on the degenerate boundary

Decay estimates for a degenerate wave equation with a dynamic fractional feedback acting on the degenerate boundary

The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect

On the Stability of a Degenerate Wave Equation Under Fractional Feedbacks Acting on the Degenerate Boundary

Contact Info

Product

Resources

About