Delayed stabilization of the Korteweg–de Vries equation on a star-shaped network

In this work, we deal with the exponential stability of nonlinear Korteweg–de Vries equation on a finite star-shaped network in presence delayed internal feedback. We start by proving well-posedness system and some regularity results. Then, state an stabilization result using Lyapunov function imposing small initial data restriction over lengths. part also, are able to obtain explicit expression for decay rate. prove semi-global result, which is based observability inequality working directly system. Next, study case where it may happen that control domain delay outside without delay. case, also local result. Finally, present numerical simulations illustrate stabilization.