On the global controllability of the 1-D Boussinesq equation

Abstract

<p style='text-indent:20px;'>We prove in this paper the global approximate controllability of the 1-D Boussinesq equation-subjected to internal control and free boundary conditions-on a bounded domain. The key ingredients of the proof relies Coron's return method for the exact global controllability of the nonlinear control system <inline-formula><tex-math id="M1">\begin{document}$ y_{tt}+(y^2)_{xx} = u(t) $\end{document}</tex-math></inline-formula>, combined with some priori estimates for nonlinear weak-hyperbolic systems defined respectively in Gevrey class of functions, and in Sobolev spaces.</p>