Asymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equation on \(\mathbb{R}^n\)
type: Item
instance of: scholarly article
title: Asymptotic behavior of spreading fronts in the anisotropic Allen-Cahn equation on \(\mathbb{R}^n\)
zbMATH Open document ID: 1411.35161
author: Hiroshi Matano
author: Yoichiro Mori
author: Mitsunori Nara
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2019-03-27T00:00:00Z
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 7043342
zbMATH Keywords: anisotropic Allen-Cahn equation
zbMATH Keywords: spreading front
zbMATH Keywords: stability
zbMATH Keywords: anisotropic mean curvature flow
zbMATH Keywords: Wulff shape
MaRDI profile type: Publication
full work available at URL: j.anihpc.2018.07.003
OpenAlex ID: W2884659719
cites work: Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen–Cahn equation
cites work: Bounds for the fundamental solution of a parabolic equation
cites work: Multidimensional nonlinear diffusion arising in population genetics
cites work: Q4661847
cites work: Anisotropic motion by mean curvature in the context of Finsler geometry
cites work: Some results on surface measures in calculus of variations
cites work: Q3057559
cites work: Generalized Transition Waves and Their Properties
cites work: Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
cites work: Anisotropic phase field equations of arbitrary order
cites work: Interface conditions for a phase field model with anisotropic and non-local interactions
cites work: The limit of the anisotropic double-obstacle Allen–Cahn equation
cites work: The Limit of the Fully Anisotropic Double-Obstacle Allen--Cahn Equation in the Nonsmooth Case
cites work: The approach of solutions of nonlinear diffusion equations to travelling front solutions
cites work: The Wulff theorem revisited
cites work: Motion by mean curvature from the Ginzburg-Landau \(\nabla\phi\) interface model
cites work: On anisotropic order parameter models for multi-phase systems and their sharp interface limits
cites work: On a uniform approximation of motion by anisotropic curvature by the Allen-Cahn equations
cites work: Bistable transition fronts in \(\mathbb{R}^N\)
cites work: Threshold dynamics type approximation schemes for propagating fronts
cites work: Spherically symmetric solutions of a reaction-diffusion equation
cites work: Asymptotic behaviour of a reaction-diffusion equation in higher space dimensions
cites work: Q5562267
cites work: Q4354424
cites work: Large time behavior of disturbed planar fronts in the Allen-Cahn equation
cites work: Stability of Planar Waves in the Allen–Cahn Equation
cites work: Front propagation for nonlinear diffusion equations on the hyperbolic space
cites work: The Wulff shape as the asymptotic limit of a growing crystalline interface
cites work: The Freidlin-Gärtner formula for general reaction terms
cites work: Stability of radially symmetric travelling waves in reaction-diffusion equations
cites work: Motion of a set by the curvature of its boundary
cites work: Generalized motion of a front propagating along its normal direction: a differential games approach
cites work: Nearly spherically symmetric expanding fronts in a bistable reaction-diffusion equation
DOI: 10.1016/J.ANIHPC.2018.07.003
description: scientific article; zbMATH DE number 7043342