We consider the the following fourth order
degenerate parabolic equation
The
equation arises in the lubrication
approximation regime, describing the
spreading of a thin film liquid with height
profile on a plate. We consider
the equation as free boundary problem,
defined on its positivity set. We address
existence and regularity of classical
solutions in weighted Hoelder and Sobolev
spaces.
Timothy Flaherty
2009-03-08