Blow-up behavior of solutions to a degenerate parabolic–parabolic Keller–Segel system

Kazuhiro Ishige, Philippe Laurençot, Noriko Mizoguchi

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Qualitative properties of solutions blowing up in finite time are obtained for a degenerate parabolic–parabolic Keller–Segel system, the nonlinear diffusion being of porous medium type with an exponent smaller or equal to the critical one mc: = 2 (N- 1) / N. In both cases, it is shown that only type II blow-up is possible, that is, blow-up at the same rate as backward self-similar solutions never occurs. Further information on the generation of singularities induced by mass concentration are given in the critical case.

Original languageEnglish
Pages (from-to)461-499
Number of pages39
JournalMathematische Annalen
Volume367
Issue number1-2
DOIs
Publication statusPublished - 2017 Feb 1

Keywords

  • 35B44
  • 35K51
  • 35K65

ASJC Scopus subject areas

  • Mathematics(all)

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