Uniqueness for the thin-film equation with a dirac mass as initial data

Mohamed Majdoub, Nader Masmoudi, Slim Tayachi

Research output: Contribution to journalArticlepeer-review

Abstract

We show the uniqueness of strong solutions for the thin-film equation ut +(uuxxx)x = 0 with initial data u(0) = mδ, m > 0, where δ is the Dirac mass at the origin. In particular, the solution is the source type one obtained by Smyth and Hill. The argument is based on an entropy estimate for the equation in self-similar variables.

Original languageEnglish (US)
Pages (from-to)2623-2635
Number of pages13
JournalProceedings of the American Mathematical Society
Volume146
Issue number6
DOIs
StatePublished - 2018

Keywords

  • Entropy estimates
  • Self-similar variables
  • Thin-film equation
  • Uniqueness
  • Zero contact angle

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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