On the stability of KdV equation with time-dependent delay on the boundary feedback in presence of saturated source term

Abstract

The current paper investigate the question of stabilizability of the Korteweg–de Vries equation with time-varying delay on the boundary feedback in the presence of a saturated source term. Under specific assumptions regarding the time-varying delay, we have established that the studied system is well-posed. Moreover, using an appropriate Lyapunov functional, we prove the exponential stability result. Finally, we give some conclusions.