Existence of Solutions to a Viscous Thin Film Equation - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.10, October 2018

Existence of Solutions to a Viscous Thin Film Equation ()

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Download as PDF (Size: 352KB) PP. 2119-2126

DOI: 10.4236/jamp.2018.610178 553 Downloads 1,059 Views

Author(s)

Yue Qiu^1,2, Bo Liang³

Affiliation(s)

¹Foundation Building, 765 Brownlow Hill, University of Liverpool, Liverpool, UK.
²Foundation Building, Xi’an Jiaotong-Liverpool University, Suzhou, China.
³School of Science, Dalian Jiaotong University, Dalian, China.

ABSTRACT

A fourth-order degenerate parabolic equation with a viscous term:

is studied with the initial-boundary conditions u_x=w_x=0 on {-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.

KEYWORDS

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

Share and Cite:

Qiu, Y. and Liang, B. (2018) Existence of Solutions to a Viscous Thin Film Equation. Journal of Applied Mathematics and Physics, 6, 2119-2126. doi: 10.4236/jamp.2018.610178.

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