scholarly journals Localization, smoothness, and convergence to equilibrium for a thin film equation

2014 ◽  
Vol 34 (11) ◽  
pp. 4537-4553 ◽  
Author(s):  
Süleyman Ulusoy ◽  
Eric Carlen
Keyword(s):  
Thin Film ◽  
Convergence To Equilibrium ◽  
Thin Film Equation

scholarly journals Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise

2021 ◽  
Author(s):  
Konstantinos Dareiotis ◽  
Benjamin Gess ◽  
Manuel V. Gnann ◽  
Günther Grün
Keyword(s):  
Thin Film ◽  
Energy Estimates ◽  
Approximation Procedure ◽  
Thin Film Flow ◽  
Thin Film Equations ◽  
Scalar Conservation Law ◽  
Thin Film Equation ◽  
Degenerate Parabolic ◽  
Scalar Conservation ◽  
Martingale Solutions

AbstractWe prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone and by Grün, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise.

scholarly journals Global existence for a thin film equation with subcritical mass

2017 ◽  
Vol 22 (4) ◽  
pp. 1461-1492 ◽  
Author(s):  
Jian-Guo Liu ◽  
◽  
Jinhuan Wang ◽  
Keyword(s):  
Thin Film ◽  
Global Existence ◽  
Thin Film Equation

Unstable sixth-order thin film equation: II. Global similarity patterns

Nonlinearity ◽  
2007 ◽  
Vol 20 (8) ◽  
pp. 1843-1881 ◽  
Author(s):  
J D Evans ◽  
V A Galaktionov ◽  
J R King
Keyword(s):  
Thin Film ◽  
Sixth Order ◽  
Thin Film Equation ◽  
Global Similarity
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