Duke Applied Mathematics

Publications [#244216] of Thomas P. Witelski

Papers Published

1. Bertozzi, AL; Grün, G; Witelski, TP, Dewetting films: Bifurcations and concentrations, Nonlinearity, vol. 14 no. 6 (November, 2001), pp. 1569-1592, IOP Publishing [doi]
   (last updated on 2024/04/18)

   Abstract:
   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 short-range repulsive forces are neglected. Both asymptotic analysis and numerical experiments show that this limit can concentrate mass in δ-distributions.