A viscous thin-film equation with a singular diffusion

被引：0
|
作者：
Xiting Peng
Bo Liang
Min Pang
Ying Wang
机构：
[1] Dalian Jiaotong University,School of Science
来源：
Boundary Value Problems | / 2016卷
关键词：
fourth-order parabolic; thin-film equation; entropy functional; singular diffusion;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The paper is devoted to studying a viscous thin-film equation with a singular diffusion term and the periodic boundary conditions in multidimensional space, which has a lot of applications in fluids theory such as draining of foams and the movement of contact lenses. In order to obtain the necessary uniform estimates and overcome the difficulty of a singular diffusion term, the entropy functional method is used. Finally, the existence of nonnegative weak solutions is obtained by some compactness arguments.
引用
收藏
相关论文
共 50 条
  • [41] EFFECT OF THIN-FILM STRESS ON DOPANT DIFFUSION IN SILICON
    AHN, ST
    KENNEL, HW
    PLUMMER, JD
    TILLER, WA
    JOURNAL OF THE ELECTROCHEMICAL SOCIETY, 1988, 135 (03) : C130 - C130
  • [42] Singular thin viscous sheet
    Boudaoud, A.
    Chaïeb, S.
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2001, 64 (5 I): : 1 - 050601
  • [43] Viscous thin-film flow over a round-crested weir
    Ruschak, KJ
    Weinstein, SJ
    JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME, 1999, 121 (03): : 673 - 677
  • [44] Singular Cauchy problem for the equation of flow of thin viscous films with nonlinear convection
    Taranets R.M.
    Shishkov A.E.
    Ukrainian Mathematical Journal, 2006, 58 (2) : 280 - 303
  • [45] A SINGULAR DIFFUSION EQUATION
    GOLDBERG, S
    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 58 (02) : 181 - 181
  • [46] The thin film equation with backwards second order diffusion
    Novick-Cohen, Amy
    Shishkov, Andrey
    INTERFACES AND FREE BOUNDARIES, 2010, 12 (04) : 463 - 496
  • [47] THIN-FILM
    DEPARIS, JR
    DATA PROCESSING, 1961, 3 (03): : 46 - 46
  • [48] On viscous film flows coating the interior of a tube: thin-film and long-wave models
    Camassa, Roberto
    Ogrosky, H. Reed
    JOURNAL OF FLUID MECHANICS, 2015, 772 : 569 - 599
  • [49] The thin-film equation:: recent advances and some new perspectives
    Becker, J
    Grün, G
    JOURNAL OF PHYSICS-CONDENSED MATTER, 2005, 17 (09) : S291 - S307
  • [50] The stochastic thin-film equation: Existence of nonnegative martingale solutions
    Gess, Benjamin
    Gnann, Manuel, V
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2020, 130 (12) : 7260 - 7302
12345