Composite Solutions to a Liquid Bilayer Model

This article continues the research initiated in (Jachalski et al. in SIAP 73(3):1183–1202, 2013). We derive explicit formulae for the leading order profiles of eleven types of stationary solutions to a one-dimensional two-layer thin-film liquid model considered with an intermolecular potential depending on both layer heights. The found solutions are composed of the repeated elementary blocks (bulk, contact line and ultra-thin-film ones) being consistently asymptotically matched together. We show that once considered on a finite interval with Neumann boundary conditions these stationary solutions are either dynamically stable or weakly translationally unstable. Other composite solutions are found to be numerically unstable and rather exhibit complex coarsening dynamics.