Exact boundary controllability of the Korteweg-de Vries equation with a piecewise constant main coefficient

This article proposes some interface conditions for a Korteweg-de Vries (KdV) equation with a piecewise constant main coefficient. The well-posedness of the Cauchy problem is proved by using multiplier technique and then an observability inequality for the adjoint problem is obtained. We end up this article with a result of local exact controllability of the discontinuous main coefficient KdV equation with a right Neumann boundary control provided that the length of the domain is small enough and the time of control is sufficiently large.