Publication detail

Lie symmetry analysis of a generalized steady-state lubrication equation in thin-film dynamics

English title

Lie symmetry analysis of a generalized steady-state lubrication equation in thin-film dynamics

Type

Other unclassified results

Language

en

Original abstract

The lubrication approximation is a fundamental framework in fluid mechanics for modeling the flow of thin liquid layers dominated by viscous and surface tension effects. We use Lie symmetry analysis to investigate the third-order ordinary differential equation y'''=y^{-n} representing the steady-state form of the generalized lubrication equation. We examine how the parameter $n$ affects the possibility of finding explicit solutions using invariant differentiation and by treating the equation as a first-order system. Invariant differentiation yields explicit solutions for n=5/4 and n=1/2. The first-order system yields solutions via integration by quadrature for n=5/2 and n=4/3. The results highlight the strong dependence of solution existence on the value of $n$ and provide insight into the nonlinear behavior of the film profile.

Keywords in English

Lie symmetry analysis; Invariant differentiation; Lubrication equation; Symmetry reduction

Released

2026-07-01

Publisher

Elsevier BV

Book

Communications in Nonlinear Science and Numerical Simulation

Journal

Communications in Nonlinear Science and Numerical Simulation

Pages from–to

109836–

BIBTEX


@misc{BUT201581,
  author="Dušan {Navrátil} and  {}",
  title="Lie symmetry analysis of a generalized steady-state lubrication equation in thin-film dynamics",
  booktitle="Communications in Nonlinear Science and Numerical Simulation",
  year="2026",
  journal="Communications in Nonlinear Science and Numerical Simulation",
  publisher="Elsevier BV",
  doi="10.1016/j.cnsns.2026.109836",
  issn="1007-5704",
  note="Other unclassified results"
}