A kinetic approach to comparison properties for degenerate parabolic-hyperbolic equations with boundary conditions

Kazuo Kobayashi

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    We study the comparison principle for degenerate parabolic-hyperbolic equations with initial and nonhomogeneous boundary conditions. We prove a comparison theorem for any entropy sub- and supersolution. The L1 contractivity and, therefore, uniqueness of entropy solutions has been obtained so far by some authors, but it seems that any comparison theorem is not proven. The method used there is the doubling variable technique due to Kružkov. Our method is based upon the kinetic formulation and the kinetic techniques. By developing the kinetic techniques for degenerate parabolic-hyperbolic equations with boundary conditions, we can obtain a comparison property which obviously extends the L1 contractive property.

    Original languageEnglish
    Pages (from-to)682-701
    Number of pages20
    JournalJournal of Differential Equations
    Volume230
    Issue number2
    DOIs
    Publication statusPublished - 2006 Nov 15

    Fingerprint

    Hyperbolic Equations
    Parabolic Equation
    Kinetics
    Boundary conditions
    Comparison Theorem
    Entropy
    Kinetic Formulation
    Sub- and Supersolutions
    Contractivity
    Nonhomogeneous Boundary Conditions
    Entropy Solution
    Comparison Principle
    Doubling
    Uniqueness

    Keywords

    • Comparison theorem
    • Degenerate parabolic equation
    • Entropy sub- and supersolution
    • Initial-boundary value problem
    • Kinetic formulation
    • Kinetic traces

    ASJC Scopus subject areas

    • Analysis

    Cite this

    A kinetic approach to comparison properties for degenerate parabolic-hyperbolic equations with boundary conditions. / Kobayashi, Kazuo.

    In: Journal of Differential Equations, Vol. 230, No. 2, 15.11.2006, p. 682-701.

    Research output: Contribution to journalArticle

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