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)

Abstract

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
Volume365
Issue number1
DOIs
Publication statusPublished - May 1 2010

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Self-similar Solutions
Nonexistence
Scaling
Invariant
Semilinear
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class. / Kozono, Hideo; Sugiyama, Yoshie; Takada, Ryo.

In: Journal of Mathematical Analysis and Applications, Vol. 365, No. 1, 01.05.2010, p. 60-66.

Research output: Contribution to journalArticle

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