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

Abstract

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 $H^s(\R^-)$ for $s\geq 0$ of the IBVP is established to concentrate on the $L^2(\R^-)$ controllability problem when the controls are in the Dirichlet and Newmann conditions at $x=0$.