Qualitative Behaviour of Solutions in Two Models of Thin Liquid Films

Matthew Michal, Marina Chugunova, Roman Taranets

Research output: Contribution to journalArticlepeer-review

Abstract

For the thin-film model of a viscous flow which originates from lubrication approximation and has a full nonlinear curvature term, we prove existence of nonnegative weak solutions. Depending on initial data, we show algebraic or exponential dissipation of an energy functional which implies dissipation of the solution arc length that is a well known property for a Hele-Shaw flow. For the classical thin-film model with linearized curvature term, under some restrictions on parameter and gradient values, we also prove analytically the arc length dissipation property for positive solutions. We compare the numerical solutions for both models, with nonlinear and with linearized curvature terms. In regimes when solutions develop finite time singularities, we explain the difference in qualitative behaviour of solutions.

Original languageEnglish (US)
Article number4063740
JournalInternational Journal of Differential Equations
Volume2016
DOIs
StatePublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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