Steady-state solutions of a mass-conserving bistable equation with a saturating flux

Burns, Martin and Grinfeld, Michael (2012) Steady-state solutions of a mass-conserving bistable equation with a saturating flux. Journal of Engineering Mathematics, 77. pp. 163-180. ISSN 0022-0833

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    Abstract

    We consider a mass-conserving bistable equation with a saturating flux on an interval. This is the quasilinear analogue of the Rubinstein–Steinberg equation, suitable for description of order parameter conserving solid–solid phase transitions in the case of large spatial gradients in the order parameter. We discuss stationary solutions and investigate the change in bifurcation diagrams as the mass constraint and the length of the interval are varied.