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

N1 - Funding Information:
The authors would like to express their sincere gratitude to Prof. J.J.L. Velázquez for his valuable comments. They are also indebted to the referee for his useful suggestions. The third author is partly supported by Research Fellow of the Japan Society for the Promotion of Science for Young Scientists.

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.

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U2 - 10.1016/j.jmaa.2009.09.063

DO - 10.1016/j.jmaa.2009.09.063

M3 - Article

AN - SCOPUS:73449144409

SN - 0022-247X

VL - 365

SP - 60

EP - 66

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -