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...

Full description

Saved in:
Bibliographic Details
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
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2015.05.027