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 languageEnglish
    Pages (from-to)1077-1098
    Number of pages22
    JournalNonlinear Analysis, Theory, Methods and Applications
    Volume57
    Issue number7-8
    DOIs
    Publication statusPublished - 2004 Jun

    Fingerprint

    Level-set Approach
    Mean Curvature Flow
    Degenerate Parabolic Equation
    Parabolic Partial Differential Equations
    Viscosity Solutions
    Comparison Theorem
    Boundary Problem
    Oblique
    Existence Theorem
    Initial-boundary-value Problem
    Boundary value problems
    Partial differential equations
    Parabolic Equation
    Hypersurface
    Curvature
    Boundary conditions
    Cover
    Viscosity
    Derivatives
    Derivative

    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

    Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. / Ishii, Hitoshi; Sato, Moto Hiko.

    In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 57, No. 7-8, 06.2004, p. 1077-1098.

    Research output: Contribution to journal › Article

    Ishii, H & Sato, MH 2004, 'Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain', Nonlinear Analysis, Theory, Methods and Applications, vol. 57, no. 7-8, pp. 1077-1098. https://doi.org/10.1016/j.na.2004.04.003
    Ishii H, Sato MH. Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. Nonlinear Analysis, Theory, Methods and Applications. 2004 Jun;57(7-8):1077-1098. https://doi.org/10.1016/j.na.2004.04.003
    Ishii, Hitoshi ; Sato, Moto Hiko. / Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. In: Nonlinear Analysis, Theory, Methods and Applications. 2004 ; Vol. 57, No. 7-8. pp. 1077-1098.
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