Stabilization results for delayed KdV equation with internal saturation

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.