Some special solutions of the thin-film equation. (Q1848337)

The authors investigate the model of a one-dimensional thin liquid film given by (\(h\) is the film height) \(\partial_t h+ \partial_x(h^3\partial^3_{xxx}h)=0\) in the basic region and \(h=KV,\;h\partial^2_{xx}h=0,\;h^3\partial^3_{xxx} h-V=0\) at the interface separating the basic from the contour region. They show the existence of solutions for the above problem. For some special conditions at the interface they prove the existence of solutions which do not have a physical meaning in the limit \(h=0\).