  We consider the Kawahara equation, a fifth order Korteweg-de Vries type
equation, posed on a bounded interval. The first result of the article is
related to the well-posedness in weighted Sobolev spaces, which one was shown
using a general version of the Lax--Milgram Theorem. With respect to the
control problems, we will prove two results. First, if the control region is a
neighborhood of the right endpoint, an exact controllability result in weighted
Sobolev spaces is established. Lastly, we show that the Kawahara equation is
controllable by regions on $L^2$ Sobolev space, the so-called regional
controllability, that is, the state function is exact controlled on the left
part of the complement of the control region and null controlled on the right
part of the complement of the control region.
