Global weak solutions to a higher order nonlinear degenerate parabolic equation

Our aim in this paper is to investigate the existence for a sixth-order parabolic equation, which arises in oil-water-surfactant mixtures. More precisely, under suitable assumptions, first we study the existence and regularity of weak solutions to an initial-boundary problem for a non-degenerate sixth-order parabolic equation. Second considering the limits of the solutions obtained in the first step, we prove the existence of weak solutions.