On the strong maximum principle and the large time behavior of generalized mean curvature flow with the Neumann boundary condition
type: Item
instance of: scholarly article
title: On the strong maximum principle and the large time behavior of generalized mean curvature flow with the Neumann boundary condition
zbMATH Open document ID: 0930.35029
author: Yoshikazu Giga
author: Masaki Ohnuma
author: Moto-Hiko Sato
published in: Journal of Differential Equations
publication date: 1999-05-17T00:00:00Z
review text: The problem studied can be written as \[ \begin{cases} u_t=|\nabla u|\cdot \text{div}({\nabla u\over|\nabla u|})\quad &\text{in }\Omega\times (0,\infty),\\ {\partial u\over\partial n}= 0\quad &\text{on }\partial\Omega\times (0,\infty),\\ u(x,0)= a(x).\end{cases} \] Here \(\Omega\) is a smooth convex domain in \(\mathbb{R}^n\). They prove a convergence result and a maximum principle for viscosity solutions.
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 1288032
zbMATH Keywords: convex domain
zbMATH Keywords: viscosity solutions
reviewed by: René Sperb
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3569
OpenAlex ID: W1963623395
cites work: A geometric heat flow for one-forms on three dimensional manifolds
cites work: Mean curvature flow through singularities for surfaces of rotation
cites work: Convergence to translating solutions for a class of quasilinear parabolic boundary problems
cites work: Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle
cites work: Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
cites work: Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
cites work: Motion of level sets by mean curvature. I
cites work: Q4861793
cites work: Q4389668
cites work: Generalized interface evolution with the Neumann boundary condition
cites work: Neumann problem for singular degenerate parabolic equations
cites work: Q4040640
cites work: Q5688819
cites work: Non-parametric mean curvature evolution with boundary conditions
cites work: A strong maximum principle for singular minimal hypersurfaces
cites work: Equilibrium solutions to generalized motion by mean curvature
cites work: Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations
cites work: Q5533735
cites work: Q4321153
cites work: Capillary problem for singular degenerate parabolic equations on a half space
cites work: Q3496846
cites work: Maximum principles and their applications
cites work: Generalized motion by curvature with a Dirichlet condition
DOI: 10.1006/JDEQ.1998.3569
description: scientific article; zbMATH DE number 1288032