Asymptotic behaviour of the thin film equation in bounded domains

Mark Bowen, J. R. King

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We investigate the extinction behaviour of a fourth order degenerate diffusion equation in a bounded domain, the model representing the flow of a viscous fluid over edges at which zero contact angle conditions hold. The extinction time may be finite or infinite and we distinguish between the two cases by identification of appropriate similarity solutions. In certain cases, an unphysical mass increase may occur for early time and the solution may become negative; an appropriate remedy for this is noted. Numerical simulations supporting the analysis are included.

Original languageEnglish
Pages (from-to)135-157
Number of pages23
JournalEuropean Journal of Applied Mathematics
Volume12
Issue number2
DOIs
Publication statusPublished - 2001
Externally publishedYes

Fingerprint

Zero angle
Thin Film Equation
Extinction Time
Degenerate Diffusion
Degenerate Equations
Similarity Solution
Contact Angle
Viscous Fluid
Diffusion equation
Extinction
Contact angle
Fourth Order
Bounded Domain
Asymptotic Behavior
Thin films
Numerical Simulation
Fluids
Computer simulation
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Asymptotic behaviour of the thin film equation in bounded domains. / Bowen, Mark; King, J. R.

In: European Journal of Applied Mathematics, Vol. 12, No. 2, 2001, p. 135-157.

Research output: Contribution to journalArticle

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