Stability results for the KdV equation with time-varying delay

Parada, Hugo; Timimoun, Chahnaz; Valein, Julie

doi:10.1016/j.sysconle.2023.105547

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Cited by 4 publications

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“…Additionally, Chentouf and Guesmia [13] studied the stability problem for the KdV equation subject to the effect of a distributed infinite memory term. Recently, in [34], Parada et al studied the stabilization problem of the KdV equation with either a boundary or distributed time-dependent delay. Note that this outcome extends those obtained in [4,36].…”

Section: Introductionmentioning

confidence: 99%

On the stability of the Kawahara equation with a distributed infinite memory

Capistrano–Filho,

Chentouf,

Jesus

2023

MCRF

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This article deals with the stability problem for a higher-order dispersive model governed by the so-called Kawahara equation. To do so, a damping mechanism is introduced, which contains a distributed memory term, and then proves that the solutions of the system are exponentially stable, provided that specific assumptions on the memory kernel are fulfilled. This is possible thanks to the energy method that permits us to obtain a decay rate estimate of the energy of the problem.

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