Null Controllability with Constraints on the State for the Korteweg-de Vries Equation

This paper is concerned with a null controllability problem for the Korteweg-de Vries equation with finite number of constraints on the state. We first let the equation evolve freely on a small time interval. Then, we consider the linearized system on the rest interval. Transforming the linearized problem into an equivalent problem of null controllability with constraints on the control, we solve the equivalent problem using an adapted Carleman estimate. Finally, by a fixed-point argument, we obtain the main result.