Global Approximate Controllability of the Korteweg-de Vries Equation by a Finite-Dimensional Force

摘要

In this paper, we consider the Korteweg-de Vries equation posed on the periodic domain T. We show that the Korteweg-de Vries equation is globally approximately controllable by a two dimensional external force. The proof is based on the Agrachev-Sarychev approach in geometric control theory.