A stability property for the generalized mean curvature flow equation
type: Item
instance of: scholarly article
title: A stability property for the generalized mean curvature flow equation
zbMATH Open document ID: 0957.35072
author: Fabio Camilli
published in: Advances in Differential Equations
publication date: 2001-03-16T00:00:00Z
review text: The author studies stability properties for interfaces generated by viscosity solutions of geometric equations. An equation \(u_t-F(x,t,Du,D^2u)=0\) for \((x,t)\in \mathbb{R}^n\times(0,\infty)\) and initial datum \(u(x,0)=u_0(x)\) is called geometric, if the function \(F:\mathbb{R}^n\times \mathbb{R}^+\times \mathbb{R}^n\times S^n\to \mathbb{R}\) satisfies the condition \(F(x,t,\lambda p, \lambda X+\mu(p\otimes p)) =\lambda F(x,t,p,X)\) for any \(\lambda>0\), \(\mu\in \mathbb{R}\), \((x,t,p,X)\in \mathbb{R}^n\times \mathbb{R}^+\times \mathbb{R}^n\times S^n\). A typical example for a geometric equation is the mean curvature flow equation. If the interface is regular, the author proves the stability of the signed distance function in front of geometric perturbations of the equation.
reviewed by: Knut Smoczyk
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 49L25
zbMATH DE Number: 1449034
zbMATH Keywords: stability of the signed distance function
zbMATH Keywords: geometric perturbations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1449034