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Session 23. Nonlinear Evolution Equations and their Applications
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Weak Solutions to Lubrication Systems Describing the Evolution of Bilayer Thin Films |
Sebastian Jachalski, Weierstrass Institute for Applied Analysis and Stochastics, Germany
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We prove existence of global non-negative weak solutions for coupled
one-dimensional lubrication systems that describe the evolution of
nanoscopic bilayer thin polymer films. We consider Navier-slip and
no-slip conditions at both liquid-liquid and liquid-solid
interfaces. Additionally, we show existence of positive smooth
solutions when attractive van der Waals and repulsive Born
intermolecular interactions are taken into account. This is a joint
work with Georgy Kitavtsev and Roman Taranets.
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