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.