  We investigate the large time behavior of compactly supported solutions for a
one-dimensional thin-film equation with linear mobility in the regime of
partial wetting. We show the stability of steady state solutions. The proof
uses the Lagrangian coordinates. Our method is to establish and exploit
differential relations between the energy and the dissipation as well as some
interpolation inequalities. Our result is different from earlier results
because here we consider solutions with finite mass.
