Global controllability of the Kawahara equation at any time

Abstract

In this article, we prove that the nonlinear Kawahara equation on the periodic domain $T$ (the unit circle in the plane) is globally approximately controllable in $H_0^s\left(T\right)$ for $s\ge 0$, at any time $T>0$, using a two-dimensional control force. The proof is based on the Agrachev–Sarychev approach in geometric control theory.