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

Burns, Martin and Grinfeld, Michael (2011) Steady state solutions of a bi-stable quasi-linear equation with saturating flux. European Journal of Applied Mathematics, 22 (4). pp. 317-331. ISSN 0956-7925

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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