### 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 language | English |
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Pages (from-to) | 60-66 |

Number of pages | 7 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 365 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2010 May 1 |

Externally published | Yes |

### Keywords

- Backward type
- Keller-Segel system
- Scaling invariance
- Self-similar solution

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Kozono, H., Sugiyama, Y., & Takada, R. (2010). Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class.

*Journal of Mathematical Analysis and Applications*,*365*(1), 60-66. https://doi.org/10.1016/j.jmaa.2009.09.063