Small-time local stabilization for a Korteweg–de Vries equation

This paper focuses on the (local) small-time stabilization of a Korteweg–de Vries equation on bounded interval, thanks to a time-varying Dirichlet feedback law on the left boundary. Recently, backstepping approach has been successfully used to prove the null controllability of the corresponding linearized system, instead of Carleman inequalities. We use the “adding an integrator” technique to gain regularity on boundary control term which clears the difficulty from getting stabilization in small time.