Dewetting films: bifurcations and concentrations

Under the influence of long-range attractive and short-range repulsive forces, thin liquid films rupture and form complex dewetting patterns. This paper studies this phenomenon in one space dimension within the framework of fourth-order degenerate parabolic equations of lubrication type. We derive the global structure of the bifurcation diagram for steady-state solutions. A stability analysis of the solution branches and numerical simulations suggest coarsening occurs. Furthermore, we study the behaviour of solutions in the limit that shortrange repulsive forces are neglected. Both asymptotic analysis and numerical experiments show that this limit can concentrate mass in δ-distributions. Mathematics Subject Classification: 34B15, 35G25, 35K55, 35Q35