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Optimal profiles in a phase-transition model with a saturating flux

It is well known that for the Allen–Cahn equation, the minimizing transition in an infinite cylinder R×ω is one-dimensional and unique up to a translation in the first variable. We analyze in this paper the existence and symmetry of optimal profiles for transitions in a similar phase-separation mode...

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Published in:	Nonlinear analysis 2015-09, Vol.125, p.334-357, Article 334
Main Authors:	Bonheure, Denis, Obersnel, Franco
Format:	Article
Language:	English
Subjects:	1D-symmetry Cylinders Dirichlet problem Double well potential Flux Flux-limited diffusion Increasing rearrangement Locally bounded variation function Mathematical analysis Mathematical models Optimization Prescribed mean curvature equation Quasilinear partial differential equation Symmetry Translations
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description	It is well known that for the Allen–Cahn equation, the minimizing transition in an infinite cylinder R×ω is one-dimensional and unique up to a translation in the first variable. We analyze in this paper the existence and symmetry of optimal profiles for transitions in a similar phase-separation model with a saturating flux. This amounts to consider transitions in the space of BV functions as we consider the area integral instead of the Dirichlet energy to penalize the creation of wild interfaces.
doi_str_mv	10.1016/j.na.2015.05.027
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subjects	1D-symmetry Cylinders Dirichlet problem Double well potential Flux Flux-limited diffusion Increasing rearrangement Locally bounded variation function Mathematical analysis Mathematical models Optimization Prescribed mean curvature equation Quasilinear partial differential equation Symmetry Translations
title	Optimal profiles in a phase-transition model with a saturating flux
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