Asymptotic profile of blow-up solutions of Keller-Segel systems in super-critical cases

Yoshie Sugiyama

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We deal with (KS)m below for the super-critical cases of q ≥ m+ 2/N with N ≥ 2, m ≥ 1; q ≥ 2. Based on an ε-regularity theorem in [20], we prove that the set Su of blow-up points of the weak solution u consists of finitely many points if {equation presented}. Moreover, we show that {equation presented} forms a delta-function singularity at the blow-up time. Simultaneously, we give a suficient condition on u such that {equation presented}. Our condition exhibits a scaling invariant class associated with (KS)m.

Original languageEnglish
Pages (from-to)601-618
Number of pages18
JournalDifferential and Integral Equations
Volume23
Issue number7-8
Publication statusPublished - Jul 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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