Communications in Mathematical Sciences
Volume 12 (2014)
Weak solutions to lubrication systems describing the evolution of bilayer thin films
Pages: 527 – 544
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.
bilayer systems, lubrication equations, weak solutions, slippage
2010 Mathematics Subject Classification
35D30, 76A20, 76D08