Uniqueness and existence for anisotropic degenerate parabolic equations with boundary conditions on a bounded rectangle

Kazuo Kobayashi*, Hiroki Ohwa

*この研究の対応する著者

    研究成果: Article査読

    32 被引用数 (Scopus)

    抄録

    We study the comparison principle for anisotropic degenerate parabolic-hyperbolic equations with initial and nonhomogeneous boundary conditions. We prove a comparison theorem for any entropy sub- and super-solution, which immediately deduces the L1 contractivity and therefore, uniqueness of entropy solutions. The method used here is based upon the kinetic formulation and the kinetic techniques developed by Lions, Perthame and Tadmor. By adapting and modifying those methods to the case of Dirichlet boundary problems for degenerate parabolic equations we can establish a comparison property. Moreover, in the quasi-isotropic case the existence of entropy solutions is proved.

    本文言語English
    ページ(範囲)137-167
    ページ数31
    ジャーナルJournal of Differential Equations
    252
    1
    DOI
    出版ステータスPublished - 2012 1 1

    ASJC Scopus subject areas

    • 分析

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