Null controllability with constraints on the state for the linear Korteweg-de Vries equation

This paper is concerned with a null controllability problem for the linear Korteweg-de Vries equation with finite number of constraints on the state. First, we prove an adapted Carleman inequality, then we transform the controllability problem with constraints on the state into an equivalent controllability problem with constraint on the control, and solve the equivalent problem by the adapted Carleman inequality.