Controllability and Stabilizability of a Higher Order Wave Equation on a Periodic Domain.

This article studies internal control of the sixth order Boussinesq equation u(tt)-u(xx) + beta u(uxxxx) - u(xxxxxx) + (u(2))(xx) = f posed on a periodic domain U with the internal control input f(., t) acting on an arbitrarily small open subset of the domain T. It is shown that the system is locally exactly controllable and exponentially stabilizable in the classic Sobolev space Hs+3(T) x H-s(T) for any s >= 0.