Composite Solutions to the Liquid Bilayer Models

Georgy Kitavtsev

In this talk I will review the research initiated in Jachalski et. al SIAP 73(3), 2014 on the two-layer thin-film liquid models considered with an intermolecular potential depending on both layer heights. The explicit formulae for the leading order profiles of eleven types of stationary solutions to these models will be derived. The found solutions are composed of the repeated elementary blocks (bulk, contact line and ultra-thin film ones) being consistently asymptotically matched together. Once considered in 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 undergo the complex coarsening dynamics.