Moving-boundary and fixed-domain problems for a sixth-order thin-film equation

We examine a number of initial boundary value problems for a paradigm sixth-order degenerate parabolic equation of the form h_t=(h^n h(xxxxx))_x which arises when considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. Analytical and numerical methods are exploited to characterise the solutions, which turn out to be rather sensitive to the value of n.