Steady-state solutions of a mass-conserving bistable equation with a saturating flux

Martin Burns, Michael Grinfeld

Research output: Contribution to journalArticle

Abstract

We consider a mass-conserving bistable equation with a saturating flux on an interval. This is the quasilinear analogue of the Rubinstein–Steinberg equation, suitable for description of order parameter conserving solid–solid phase transitions in the case of large spatial gradients in the order parameter. We discuss stationary
solutions and investigate the change in bifurcation diagrams as the mass constraint and the length of the interval are varied.
LanguageEnglish
Pages163-180
Number of pages18
JournalJournal of Engineering Mathematics
Volume77
DOIs
Publication statusPublished - 2012

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Steady-state Solution
Order Parameter
Fluxes
Interval
Bifurcation Diagram
Phase Transition
Phase transitions
Gradient
Analogue

Keywords

  • bifurcation
  • classical and non-classical solutions
  • Liapunov-Schmidt reduction
  • quadilinear parabolic equation

Cite this

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Steady-state solutions of a mass-conserving bistable equation with a saturating flux. / Burns, Martin; Grinfeld, Michael.

In: Journal of Engineering Mathematics, Vol. 77, 2012, p. 163-180.

Research output: Contribution to journalArticle

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