Two generalisations of the thin film equation

This paper is concerned with two generalisations of the widely studied thin film equation ut = −(unuxxx)x. Both are degenerate fourth-order parabolic equations in conservation form; the first is which shares the scaling properties of the thin film equation (with special cases arising in applications and in earlier analyses), while the second is a doubly nonlinear equation which is relevant to capillary driven flows of thin films of power-law fluids. We focus on giving a characterisation of nonnegative mass preserving compactly supported solutions, exploiting local analyses about the edge of the support and special closed form solutions; however, other properties are also noted and open questions raised.