Weak solutions to lubrication systems describing the evolution of bilayer thin films

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Jachalski S., Kitavtsev G., Taranets R.

Communications in Mathematical Sciences, vol.12, no.3, pp.527-544, 2014 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.4310/cms.2014.v12.n3.a7
  • Journal Name: Communications in Mathematical Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.527-544
  • Keywords: Bilayer systems, Lubrication equations, Slippage, Weak solutions
  • Open Archive Collection: AVESIS Open Access Collection
  • Middle East Technical University Northern Cyprus Campus Affiliated: No

Abstract

The existence of global non-negative weak solutions is proved for coupled onedimensional lubrication systems that describe the evolution of nanoscopic bilayer thin polymer films that take account of Navier-slip or no-slip conditions at both liquid-liquid and liquid-solid interfaces. In addition, in the presence of attractive van derWaals and repulsive Born intermolecular interactions existence of positive smooth solutions is shown. © 2014 International Press.