Liang, B. and Zheng, S. (2008) Existence and Asymptotic Behavior of Solutions to a Nonlinear Parabolic Equation of Fourth Order. Journal of Mathematical Analysis and Applications, 348, 234-243.
https://doi.org/10.1016/j.jmaa.2008.07.022

has been cited by the following article:

• TITLE: Existence of Solutions to a Viscous Thin Film Equation

  AUTHORS: Yue Qiu, Bo Liang

  KEYWORDS: Fourth-Order Degenerate Parabolic, Thin Film Equation, Cahn-Hilliard Equation, Entropy Functional

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.10, October 26, 2018

  ABSTRACT: A fourth-order degenerate parabolic equation with a viscous term: is studied with the initial-boundary conditions ux=wx=0on {-1,1}×(0,T), u(x,0)=u0(x)in (-1,1). It can be taken as a thin film equation or a Cahn-Hilliard equation with a degenerate mobility. The entropy functional method is introduced to overcome the difficulties that arise from the degenerate mobility m(u)and the viscosity term. The existence of nonnegative weak solution is obtained.