@article{895e250c2f9446f181009d1e871d168d,

title = "Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class",

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.",

keywords = "Backward type, Keller-Segel system, Scaling invariance, Self-similar solution",

author = "Hideo Kozono and Yoshie Sugiyama and Ryo Takada",

note = "Funding Information: The authors would like to express their sincere gratitude to Prof. J.J.L. Vel{\'a}zquez 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.",

year = "2010",

month = may,

day = "1",

doi = "10.1016/j.jmaa.2009.09.063",

language = "English",

volume = "365",

pages = "60--66",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}