Stability of planar fronts for a non-local phase kinetics equation with a conservation law in \(D \leq 3\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1252.35060
DOI: 10.1142/S0129055X12500092
published in: Reviews in Mathematical Physics
publication date: 2012-06-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1107.5189
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 6050827
zbMATH Keywords: nonlinear stability
zbMATH Keywords: nonlocal and nonlinear evolution equation
zbMATH Keywords: local magnetization
zbMATH Keywords: Gates-Penrose-Lebowitz free energy
zbMATH Keywords: sub-critical temperatures
zbMATH Keywords: two local spatially homogeneous equilibria
author: Eric Carlen
author: Enza Orlandi
MaRDI profile type: Publication
arXiv ID: 1107.5189
cites work: A nonlocal anisotropic model for phase transitions
cites work: Tunneling in two dimensions
cites work: Algebraic rate of decay for the excess free energy and stability of fronts for a nonlocal phase kinetics equation with a conservation law. I
cites work: Algebraic Rate of Decay for The Excess Free Energy And Stability of Fronts for A Nonlocal Phase Kinetics Equation with A Conservation Law,Ii
cites work: A simple proof of stability of fronts for the Cahn-Hilliard equation
cites work: Travelling fronts in non-local evolution equations
cites work: Stability of the interface in a model of phase separation
cites work: Phase segregation dynamics in particle systems with long range interactions. I: Macroscopic limits
cites work: Elliptic Partial Differential Equations of Second Order
cites work: Anomalous scaling for three‐dimensional Cahn‐Hilliard fronts
cites work: Scaling limits in statistical mechanics and microstructures in continuum mechanics
OpenAlex ID: W3102578808
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title: Stability of planar fronts for a non-local phase kinetics equation with a conservation law in \(D \leq 3\)
review text: The authors study a nonlocal and nonlinear evolution equation, in a cylinder, describing the dynamics of a local magnetization process. Here, a basic tool is represented by the Gates-Penrose-Lebowitz free energy functional defined on the measurable functions of the cylinder through which the considered equation is written in a gradient flow form. It is shown that for sub-critical temperatures there are two local spatially homogeneous equilibria. A stability result for the planar fronts is established.
reviewed by: Dumitru Motreanu
description: scientific article; zbMATH DE number 6050827