Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller-Segel system

Hideo Kozono, Yoshie Sugiyama, Yumi Yahagi

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    In Rn (n≥ 3), we first define a notion of weak solutions to the Keller-Segel system of parabolic-elliptic type in the scaling invariant class Ls(0,T;L r(R n)) for 2/ s + n/ r = 2 with n/2 < r< n. Any condition on derivatives of solutions is not required at all. The local existence theorem of weak solutions is established for every initial data in L n/2(R n). We prove also their uniqueness. As for the marginal case when r= n/2, we show that if n≥ 4, then the class C([0,T);L n/2(R n)) enables us to obtain the only weak solution.

    Original languageEnglish
    Pages (from-to)2295-2313
    Number of pages19
    JournalJournal of Differential Equations
    Volume253
    Issue number7
    DOIs
    Publication statusPublished - 2012 Oct 1

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    Existence and Uniqueness Theorem
    Weak Solution
    Local Existence
    Existence Theorem
    Uniqueness
    Scaling
    Derivative
    Invariant
    Derivatives
    Class

    ASJC Scopus subject areas

    • Analysis

    Cite this

    Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller-Segel system. / Kozono, Hideo; Sugiyama, Yoshie; Yahagi, Yumi.

    In: Journal of Differential Equations, Vol. 253, No. 7, 01.10.2012, p. 2295-2313.

    Research output: Contribution to journalArticle

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