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

Research output: Contribution to journal › Article

18 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1077-1098
Number of pages	22
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	57
Issue number	7-8
DOIs	https://doi.org/10.1016/j.na.2004.04.003
Publication status	Published - 2004 Jun

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Keywords

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

ASJC Scopus subject areas

Analysis
Applied Mathematics
Mathematics(all)

Cite this

Ishii, H., & Sato, M. H. (2004). Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. Nonlinear Analysis, Theory, Methods and Applications, 57(7-8), 1077-1098. https://doi.org/10.1016/j.na.2004.04.003

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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.

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KW - Neumann-type boundary conditions

KW - Singular degenerate parabolic equations

KW - Viscosity solutions

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Access to Document

10.1016/j.na.2004.04.003