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 language | English |
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Pages (from-to) | 461-499 |
Number of pages | 39 |
Journal | Mathematische Annalen |
Volume | 367 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2017 Feb 1 |
Keywords
- 35B44
- 35K51
- 35K65
ASJC Scopus subject areas
- Mathematics(all)