Composite Solutions to a Liquid Bilayer Model

KITAVTSEV G.

Journal of Nonlinear Science, cilt.35, sa.1, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s00332-024-10108-5
  • Dergi Adı: Journal of Nonlinear Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: 35B36, 35C20, 35G61, 76D08, 76D45, Bilayer systems, Coarsening, Intermolecular potential, Stationary solutions
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.