  In this technical report, we consider a nonlinear 4th-order degenerate
parabolic partial differential equation that arises in modelling the dynamics
of an incompressible thin liquid film on the outer surface of a rotating
horizontal cylinder in the presence of gravity. The parameters involved
determine a rich variety of qualitatively different flows. Depending on the
initial data and the parameter values, we prove the existence of nonnegative
periodic weak solutions. In addition, we prove that these solutions and their
gradients cannot grow any faster than linearly in time; there cannot be a
finite-time blow-up. Finally, we present numerical simulations of solutions.
