  The degenerate parabolic equation u_t + [u^3(u_xxx + u_x - sin x)]_x=0 models
the evolution of a thin liquid film on a stationary horizontal cylinder. It is
shown here that for each given mass there is a unique steady state, given by a
droplet hanging from the bottom of the cylinder that meets the dry region at
the top with zero contact angle. The droplet minimizes the energy and attracts
all strong solutions that satisfy certain energy and entropy inequalities. The
distance of any solution from the steady state decays no faster than a power
law.
