scholarly journals Strong Solutions of the Thin Film Equation in Spherical Geometry

2018 ◽  
pp. 181-192
Author(s):  
Roman M. Taranets
Keyword(s):  
Thin Film ◽  
Spherical Geometry ◽  
Strong Solutions ◽  
Thin Film Equation

Strong solutions and trajectory attractors to the thin-film equation with absorption

2021 ◽  
Vol 493 (2) ◽  
pp. 124562
Author(s):  
Oleksiy V. Kapustyan ◽  
Pavlo O. Kasyanov ◽  
Roman M. Taranets
Keyword(s):  
Thin Film ◽  
Strong Solutions ◽  
Thin Film Equation ◽  
Trajectory Attractors

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
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