Nonclassical symmetry solutions for fourth-order phase field reaction-diffusion
type: Item
instance of: scholarly article
title: Nonclassical symmetry solutions for fourth-order phase field reaction-diffusion
zbMATH Open document ID: 1392.35180
author: Philip Broadbridge
author: Dimetre Triadis
author: Dilruk Gallage
author: Pierluigi Cesana
published in: Symmetry
publication date: 2018-08-13T00:00:00Z
review text: Summary: Using the nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing phase of cylindrical or spherical inclusion, allowing for a ``mushy'' zone with a mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 6916699
zbMATH Keywords: fourth-order diffusion
zbMATH Keywords: Allen-Cahn equation
zbMATH Keywords: Cahn-Hilliard equation
zbMATH Keywords: phase field
zbMATH Keywords: nonlinear reaction-diffusion
MaRDI profile type: Publication
full work available at URL: sym10030072
OpenAlex ID: W2782706101
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Wikidata QID: Q130089734
DOI: 10.3390/SYM10030072
description: scientific article; zbMATH DE number 6916699