Steady states and dynamics of a thin-film-type equation with non-conserved mass

Published online

Journal Article

We study the steady states and dynamics of a thin-film-type equation with non-conserved mass in one dimension. The evolution equation is a non-linear fourth-order degenerate parabolic partial differential equation (PDE) motivated by a model of volatile viscous fluid films allowing for condensation or evaporation. We show that by changing the sign of the non-conserved flux and breaking from a gradient flow structure, the problem can exhibit novel behaviours including having two distinct classes of co-existing steady-state solutions. Detailed analysis of the bifurcation structure for these steady states and their stability reveals several possibilities for the dynamics. For some parameter regimes, solutions can lead to finite-time rupture singularities. Interestingly, we also show that a finite-amplitude limit cycle can occur as a singular perturbation in the nearly conserved limit.

Full Text

Duke Authors

Cited Authors

  • JI, HANGJIE; WITELSKI, THOMASP

Published In

Start / End Page

  • 1 - 34

Published By

Electronic International Standard Serial Number (EISSN)

  • 1469-4425

International Standard Serial Number (ISSN)

  • 0956-7925

Digital Object Identifier (DOI)

  • 10.1017/s0956792519000330

Language

  • en