  In this paper we consider the fourth order operators A1u := (au")" and A2u :=
au"" in divergence form and non divergence form, respectively, where a, defined
in [0, 1] with values in R+, degenerates in an interior point of the interval.
Using the semigroup technique, under suitable assumptions on a, we study the
generation property of these operators associated to generalized Wentzell
boundary conditions, proving the well posedness of the corresponding parabolic
problems.
