Weak solutions to lubrication systems describing the evolution of bilayer thin films
Analysis of PDEs
2012-11-12 v1
Abstract
The existence of global nonnegative weak solutions is proved for coupled one-dimensional 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 der Waals and repulsive Born intermolecular interactions existence of positive smooth solutions is shown.
Cite
@article{arxiv.1211.2216,
title = {Weak solutions to lubrication systems describing the evolution of bilayer thin films},
author = {Sebastian Jachalski and Georgy Kitavtsev and Roman Taranets},
journal= {arXiv preprint arXiv:1211.2216},
year = {2012}
}