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prescribed mean curvature equation

European Journal of Applied Mathematics (1)

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Steady state solutions of a bi-stable quasi-linear equation with saturating flux
M. BURNS, M. GRINFELD
Journal:

European Journal of Applied Mathematics / Volume 22 / Issue 4 / August 2011

Published online by Cambridge University Press:

17 February 2011, pp. 317-331
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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.