$L^2-$ Well-posedness and Bounded Controllability of KdV-B equation

In this paper, the initial boundary value problem of the Korteweg-de Vries Burger equation on the negative half-plane is analyzed. Initially, the well-posedness on $H^s({\mathbb{R}}^{-})$ for $s\ge 0$ of the IBVP is established to concentrate on the $L^2({\mathbb{R}}^{-})$ controllability problem when the controls are in the Dirichlet and Newmann conditions at $x=0$.