Steady state solutions of a bi-stable quasi-linear equation with saturating flux

Martin Burns, Michael Grinfeld

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We consider the bistable equation proposed by Rosenau to replace the Allen-Cahn equation in the case of large gradients. We discuss the bifurcation problem for stationary solutions of this equation on an interval as the diusion coecient and the length of the interval are varied, concentrating on classical solution
LanguageEnglish
Pages317-331
Number of pages15
JournalEuropean Journal of Applied Mathematics
Volume22
Issue number4
Early online date17 Feb 2011
DOIs
Publication statusPublished - Aug 2011

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Quasilinear Equations
Steady-state Solution
Linear equations
Fluxes
Allen-Cahn Equation
Interval
Stationary Solutions
Classical Solution
Bifurcation
Gradient

Keywords

  • quasilinear parabolic equations
  • saturating
  • stationary solutions
  • prescribed mean curvature equation

Cite this

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abstract = "We consider the bistable equation proposed by Rosenau to replace the Allen-Cahn equation in the case of large gradients. We discuss the bifurcation problem for stationary solutions of this equation on an interval as the diusion coecient and the length of the interval are varied, concentrating on classical solution",
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Steady state solutions of a bi-stable quasi-linear equation with saturating flux. / Burns, Martin; Grinfeld, Michael.

In: European Journal of Applied Mathematics, Vol. 22, No. 4, 08.2011, p. 317-331.

Research output: Contribution to journalArticle

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