  In this paper the model for a highly viscous droplet sliding down an inclined
plane is analyzed. It is shown that, provided the slope is not too steep, the
corresponding moving boundary problem possesses classical solutions.
Well-posedness is lost when the relevant linearization ceases to be parabolic.
This occurs above a critical incline which depends on the shape of the initial
wetted region as well as on the liquid's mass. It is also shown that
translating circular solutions are asymptotically stable if the kinematic
boundary condition is given by an affine functionand provided the incline is
small.

Analysis of PDEs