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Abstract: We prove long--time existence for a weak solution s(t; x) 0 of the lubrication approximation @ t s + @ x (s @ 3 x s) = 0 in fs ? 0g with prescribed contact angle of, say, 4 (@ x s) 2 = 1 on @fs ? 0g : AMS code: 35K65, 35R35, 76D08, 76S05 Introduction The equation we study models an experiment we will introduce first. Our intention hereby is not to give a full description of the experiment and its various models, but to provide the reader with some intuition of the equation under... (Update)
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.... for the dynamics of nonlinear fourth order equations was thouroughly investigated in the context of lubrication type equations [2, 3, 4, 5, 7, 21]. They arise in the study of thin liquid lms and spreading droplets (for an overview see [6] and the references therein)...
...This norm can be used to describe the thin film evolution as a gradient flow in H 1 . In this context, let us also mention the paper [48] by Otto which shows that the surface tension driven thin film flow in the Hele Shaw cell has a gradient flow structure with respect to the...
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BibTeX entry: (Update)
F. Otto, Lubrication approximation with prescribed nonzero contact angle, Comm. http://citeseer.ist.psu.edu/324646.html More
@misc{ otto-lubrication,
author = "F. Otto",
title = "Lubrication approximation with prescribed nonzero contact angle",
text = "F. Otto, Lubrication approximation with prescribed nonzero contact angle,
Comm.",
url = "citeseer.ist.psu.edu/324646.html" }
Citations (may not include all citations):68 Probability metrics and the stability of stochastic models (context) - Rachev - 1991
35 Higher order nonlinear degenerate parabolic equations (context) - Bernis, Friedman - 1990
29 Polar factorization and monotone rearrangement of vector-- v.. (context) - Brenier - 1991
29 Nonnegative solutions of a fourth order nonlinear degenerate.. (context) - Beretta, Bertsch et al. - 1995
24 The lubrication approximation for thin viscous films: regula.. - Bertozzi, Pugh - 1996
23 The geometry of optimal transportation (context) - Gangbo, McCann - 1997
19 Weak convergence methods for nonlinear partial differential .. (context) - Evans - 1990
14 Droplet breakup in a model of the Hele--Shaw cell (context) - Constantin, Dupont et al. - 1993
13 The variational formulation of the Fokker--Planck equation - Kinderlehrer, Jordan et al. - 1998
12 Existence and regularity for a minimum problem with free bou.. (context) - --W, Caffarelli - 1981
11 Dynamics of labyrinthine pattern formation in magnetic fluid.. - Otto - 1998
11 A class of Wasserstein metrics for probability distributions (context) - Givens, Shortt - 1984
10 An elementary proof of the polar factorization of vector-- v.. (context) - Gangbo - 1994
8 Degenerate parabolic differential equations of fourth order .. (context) - Grun - 1995
7 Viscous flow in two dimensions (context) - Bensimon, Kadanoff et al. - 1986
7 Singularity formation in Hele--Shaw bubbles - Almgren - 1996
7 Allocation maps with general cost functions (context) - Caffarelli - 1996
4 Integral inequalities with applications to nonlinear degener.. (context) - Bernis - 1996
3 Topological transitions and singularities in viscous flows (context) - Goldstein, Pesci et al. - 1993
1 fourth order nonlinear degenerate equations and singular ell.. (context) - Bernis, flow - 1995
1 Finite--time singularity formation in Hele--Shaw systems (context) - Constantin, Goldstein et al. - 1993
1 Solutions to the two--phase Stefan problem with Gibbs-- Thom.. (context) - Luckhaus - 1990
1 On identifying the appropriate boundary conditions at a movi.. (context) - Dussan, Ram'e et al. - 1991
1 the Cahn--Hilliard equation with degenerate mobility (context) - Elliot, Garcke - 1996
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