### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*365*(1), 60-66. https://doi.org/10.1016/j.jmaa.2009.09.063

**Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class.** / Kozono, Hideo; Sugiyama, Yoshie; Takada, Ryo.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 365, no. 1, pp. 60-66. https://doi.org/10.1016/j.jmaa.2009.09.063

}

TY - JOUR

T1 - Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class

AU - Kozono, Hideo

AU - Sugiyama, Yoshie

AU - Takada, Ryo

PY - 2010/5/1

Y1 - 2010/5/1

N2 - 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.

AB - 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.

KW - Backward type

KW - Keller-Segel system

KW - Scaling invariance

KW - Self-similar solution

UR - http://www.scopus.com/inward/record.url?scp=73449144409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73449144409&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2009.09.063

DO - 10.1016/j.jmaa.2009.09.063

M3 - Article

AN - SCOPUS:73449144409

VL - 365

SP - 60

EP - 66

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -