Controllability aspects of the Korteweg-de Vries Burgers equation on unbounded domains

The aim of this work is to consider the controllability problem of the linear system associated to Korteweg-de Vries Burgers equation posed in the whole real line. We obtain a sort of exact controllability for solutions in Lloc2(R2) by deriving an internal observability inequality and a Global Carleman estimate. Following the ideas contained in [25], the problem is reduced to prove an approximate theorem.