Stabilization results for delayed  KdV equation with internal saturation

Toufik ennouari; Ahmat Mahamat  Taboye; Abdellaziz  Binid

doi:10.5269/bspm.71439

Toufik ennouari Chouaib Doukkali University
Ahmat Mahamat Taboye
Abdellaziz Binid

Abstract

In this paper, we consider the nonlinear Korteweg-de Vries equation with time-varying delay on the boundary feedback, in the presence of a saturated source term. Under specific assumptions concerning the time-varying delay, we have demonstrated that the studied system is well-posed. Furthermore, we have proven that this system is exponentially stable. Specifically, by introducing an appropriate energy and employing the Lyapunov approach, we ensure that the unique solution of the Korteweg-de Vries equation is exponentially stable. Finally, we present some conclusions.

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