  It has been established that solutions to the inviscid Proudman-Johnson
equation subject to a homogeneous three-point boundary condition can develop
singularities in finite time. In this paper, we consider the possibility of
singularity formation in solutions of the generalized, inviscid
Proudman-Johnson equation with damping subject to the same homogeneous
three-point boundary condition. In particular, we derive conditions the initial
data must satisfy in order for solutions to blowup in finite time with either
bounded or unbounded smooth damping term.
