Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class

Hideo Kozono, Yoshie Sugiyama, Ryo Takada

Research output: Contribution to journalArticle

5 Citations (Scopus)


Let us consider the problem whether there does exist a finite-time self-similar solution of the backward type to the semilinear Keller-Segel system. In the case of parabolic-elliptic type for n ≥ 3 we show that there is no such a solution with a finite mass in the scaling invariant class. On the other hand, in the case of parabolic-parabolic type for n ≥ 2, non-existence of finite-time self-similar solutions is proved in a larger class of a finite mass with some local bounds.

Original languageEnglish
Pages (from-to)60-66
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2010 May 1
Externally publishedYes



  • Backward type
  • Keller-Segel system
  • Scaling invariance
  • Self-similar solution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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