# Controllability Aspects of the Korteweg-de Vries Burgers Equation on Unbounded Domains

## TL;DR

This paper investigates the controllability of the linear Korteweg-de Vries Burgers equation on unbounded domains, establishing conditions for exact controllability through observability inequalities and Carleman estimates.

## Contribution

It introduces new controllability results for the linear Korteweg-de Vries Burgers equation on the real line, utilizing observability and Carleman estimates.

## Key findings

- Established internal observability inequality.
- Derived a global Carleman estimate.
- Achieved a form of exact controllability for the system.

## Abstract

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 $L^2_{loc}(\R^2)$ by deriving an internal observability inequality and a Global Carlemann estimate. Following the ideas contained in \cite{rosier2000}, the problem is reduced to prove an approximate theorem.