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

Published online by Cambridge University Press:  17 February 2011

M. BURNS  and
M. GRINFELD
M. BURNS
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, UK email: martin.f.burns@strath.ac.uk
M. GRINFELD
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, UK email: martin.f.burns@strath.ac.uk
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Abstract

In this paper, we consider the bi-stable 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 diffusion coefficient and the length of the interval are varied, concentrating on classical solutions.

Keywords

Prescribed mean curvature equationbi-stable non-linearitystationary solutions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 4 , August 2011 , pp. 317 - 331
Copyright
Copyright © Cambridge University Press 2011

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