The author studies the title problem by using the fourth-order degenerate diffusion equation
is the thickness of the liquid film, and
is a prescribed function related to the solution-dependent diffusion coefficient,
. First, a special discussion is devoted to the finite-time singularities and similarity solutions of a particular one-dimensional equation
. Then the author examines weak solutions of the general equation which correspond to various constitutive laws for moving contact lines (Young’s law, Greenspan-McKay law, van der Walls and superdiffusion models). Numerical results obtained by finite difference methods conclude the paper.