The self-similar solution for draining in the thin film equation

Jan Bouwe Van Den Berg, Mark Bowen, John R. King, M. M A El-Sheikh

Research output: Contribution to journalArticle

3 Citations (Scopus)


We investigate self-similar solutions of the thin film equation in the case of zero contact angle boundary conditions on a finite domain. We prove existence and uniqueness of such a solution and determine the asymptotic behaviour as the exponent in the equation approaches the critical value at which zero contact angle boundary conditions become untenable. Numerical and power-series solutions are also presented.

Original languageEnglish
Pages (from-to)329-346
Number of pages18
JournalEuropean Journal of Applied Mathematics
Issue number3
Publication statusPublished - 2004 Jun
Externally publishedYes


ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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