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

Hideo Kozono, Yoshie Sugiyama, Yumi Yahagi

研究成果: Contribution to journalArticle査読

7 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)2295-2313
ページ数19
ジャーナルJournal of Differential Equations
253
7
DOI
出版ステータス出版済み - 10 1 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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