### 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 S_{u} 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 language | English |
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Pages (from-to) | 601-618 |

Number of pages | 18 |

Journal | Differential and Integral Equations |

Volume | 23 |

Issue number | 7-8 |

Publication status | Published - Jul 2010 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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## Cite this

Sugiyama, Y. (2010). Asymptotic profile of blow-up solutions of Keller-Segel systems in super-critical cases.

*Differential and Integral Equations*,*23*(7-8), 601-618.