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

作者：Kozono Hideo^*; Sugiyama Yoshie; Takada Ryo

来源：Journal of Mathematical Analysis and Applications, 2010, 365(1): 60-66.

DOI：10.1016/j.jmaa.2009.09.063

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

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, nonexistence of finite-time self-similar solutions is proved in a larger class of a finite mass with some local bounds.

• 出版日期2010-5-1