Methods and Applications of Analysis
Volume 18 (2011)
Weak solutions to lubrication equations in the presence of strong slippage
Pages: 183 – 202
The existence of global weak solutions is proved for one-dimensional lubrication models that describe the dewetting process of nanoscopic thin polymer films on hydrophobyzed substrates and take account of large slippage at the polymer-substrate interface. The convergence of these solutions as either the Reynolds number or the capillarity goes to zero, as well as their limiting behaviour as the slip length goes to zero or infinity are investigated.
existence, thin film, lubrication equation, slippage
2010 Mathematics Subject Classification
35D30, 35M33, 35Q35, 76D08