A method of energy estimates in L and its application to porous medium equations

Mitsuharu Otani, Yoshie Sugiyama

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    The existence of time local C-solutions is shown for Cauchy problem of the porous medium equations. Our arguments rely on the "L-energy method" developed in our previous paper [16] and a new method based on the theory of evolution equations in the L2-framework which enables us to handle with porturbations which can be decomposed into monotone parts and small parts in Sobolev spaces of higher order.

    Original languageEnglish
    Pages (from-to)1-789
    Number of pages789
    JournalJournal of the Mathematical Society of Japan
    Volume53
    Issue number4
    Publication statusPublished - 2001 Oct

    Fingerprint

    Porous Medium Equation
    Energy Estimates
    Local Time
    Energy Method
    Sobolev Spaces
    Evolution Equation
    Cauchy Problem
    Monotone
    Higher Order
    Framework

    Keywords

    • C-solution
    • Evolution equation
    • Local existence
    • Nonlinear parabolic
    • Porous medium equation

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    A method of energy estimates in L and its application to porous medium equations. / Otani, Mitsuharu; Sugiyama, Yoshie.

    In: Journal of the Mathematical Society of Japan, Vol. 53, No. 4, 10.2001, p. 1-789.

    Research output: Contribution to journalArticle

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