The equivalence of weak solutions and entropy solutions of nonlinear degenerate second-order equations

Kazuo Kobayashi

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    15 Citations (Scopus)

    Abstract

    We prove the equivalence of weak solutions and entropy solutions of an elliptic-parabolic-hyperbolic degenerate equation g(t)t - Δb(u) + div φ(u) = f with homogeneous Dirichlet conditions and initial conditions. As a result of the equivalence, we obtain the L1-contraction principle and uniqueness of weak solutions of elliptic-parabolic degenerate equations.

    Original languageEnglish
    Pages (from-to)383-395
    Number of pages13
    JournalJournal of Differential Equations
    Volume189
    Issue number2
    DOIs
    Publication statusPublished - 2003 Apr 10

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    Keywords

    • Comparison
    • Degenerate elliptic-hyperbolic equation
    • Entropy solution
    • Uniqueness
    • Weak solution

    ASJC Scopus subject areas

    • Analysis

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