Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain

Hitoshi Ishii; Moto Hiko Sato

doi:10.1016/j.na.2004.04.003

Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain

Hitoshi Ishii^*, Moto Hiko Sato

^*この研究の対応する著者

研究成果: Article › 査読

23 被引用数 (Scopus)

抄録

We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial differential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature flow equation and apply to more general Neumann-type boundary problems for parabolic equations in the level set approach to motion of hypersurfaces with velocity depending on the normal direction and curvature.

本文言語	English
ページ（範囲）	1077-1098
ページ数	22
ジャーナル	Nonlinear Analysis, Theory, Methods and Applications
巻	57
号	7-8
DOI	https://doi.org/10.1016/j.na.2004.04.003
出版ステータス	Published - 2004 6月

ASJC Scopus subject areas

分析
応用数学
数学 (全般)

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10.1016/j.na.2004.04.003

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title = "Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain",

abstract = "We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial differential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature flow equation and apply to more general Neumann-type boundary problems for parabolic equations in the level set approach to motion of hypersurfaces with velocity depending on the normal direction and curvature.",

keywords = "Capillary problem, Mean curvature flow, Neumann-type boundary conditions, Singular degenerate parabolic equations, Viscosity solutions",

author = "Hitoshi Ishii and Sato, {Moto Hiko}",

year = "2004",

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doi = "10.1016/j.na.2004.04.003",

language = "English",

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T1 - Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain

AU - Ishii, Hitoshi

AU - Sato, Moto Hiko

PY - 2004/6

Y1 - 2004/6

N2 - We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial differential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature flow equation and apply to more general Neumann-type boundary problems for parabolic equations in the level set approach to motion of hypersurfaces with velocity depending on the normal direction and curvature.

AB - We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial differential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature flow equation and apply to more general Neumann-type boundary problems for parabolic equations in the level set approach to motion of hypersurfaces with velocity depending on the normal direction and curvature.

KW - Capillary problem

KW - Mean curvature flow

KW - Neumann-type boundary conditions

KW - Singular degenerate parabolic equations

KW - Viscosity solutions

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U2 - 10.1016/j.na.2004.04.003

DO - 10.1016/j.na.2004.04.003

M3 - Article

AN - SCOPUS:2942566475

SN - 0362-546X

VL - 57

SP - 1077

EP - 1098

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 7-8

ER -

Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain

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