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

Martin Burns; Michael Grinfeld

doi:10.1017/S0956792511000076

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

Martin Burns, Michael Grinfeld

Mathematics And Statistics

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29 Citations (Scopus)

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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

Original language	English
Pages (from-to)	317-331
Number of pages	15
Journal	European Journal of Applied Mathematics
Volume	22
Issue number	4
Early online date	17 Feb 2011
DOIs	https://doi.org/10.1017/S0956792511000076
Publication status	Published - Aug 2011

Keywords

quasilinear parabolic equations
saturating
stationary solutions
prescribed mean curvature equation

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title = "Steady state solutions of a bi-stable quasi-linear equation with saturating flux",

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",

keywords = "quasilinear parabolic equations, saturating, stationary solutions, prescribed mean curvature equation",

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AB - 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

KW - quasilinear parabolic equations

KW - saturating

KW - stationary solutions

KW - prescribed mean curvature equation

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DO - 10.1017/S0956792511000076

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EP - 331

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

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

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Keywords

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