scholarly journals The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations

2021 ◽  
Vol 59 (1) ◽  
pp. 60-87
Author(s):  
Julian Fischer ◽  
Daniel Matthes
Keyword(s):  
Thin Film ◽  
Porous Medium ◽  
Waiting Time ◽  
Thin Film Equations

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 Thin film flow of a second grade fluid in a porous medium past a stretching sheet with heat transfer

2018 ◽  
Vol 57 (2) ◽  
pp. 1019-1031 ◽  
Author(s):  
Noor Saeed Khan ◽  
Saeed Islam ◽  
Taza Gul ◽  
Ilyas Khan ◽  
Waris Khan ◽  
...  
Keyword(s):  
Thin Film ◽  
Heat Transfer ◽  
Porous Medium ◽  
Stretching Sheet ◽  
Film Flow ◽  
Second Grade ◽  
Thin Film Flow ◽  
Second Grade Fluid ◽  
Grade Fluid

Waiting time phenomena for the porous medium equation with gradient absorption

2014 ◽  
Vol 47 (1-2) ◽  
pp. 225-236
Author(s):  
Pan Zheng ◽  
Chunlai Mu ◽  
Fuchen Zhang ◽  
Iftikhar Ahmed
Keyword(s):  
Porous Medium ◽  
Waiting Time ◽  
Porous Medium Equation ◽  
Medium Equation

Activation field, fatigue, and waiting‐time effects in KNO3 thin‐film memories

1987 ◽  
Vol 62 (11) ◽  
pp. 4510-4513 ◽  
Author(s):  
J. F. Scott ◽  
B. Pouligny ◽  
K. Dimmler ◽  
M. Parris ◽  
D. Butler ◽  
...  
Keyword(s):  
Thin Film ◽  
Waiting Time ◽  
Time Effects
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