Recently, P. Souplet and M. Winkler [CMP, 2019] studied a simplified parabolic-elliptic Keller-Segel system in $\Omega\subset R^n (n>2)$. They obtained the blow-up profile $cr^{-2}\le U(r) \le Cr^{-2}$ under suitable conditions, where  $U(r)=\lim_{t\rightarrow T}u(r,t)$. An open problem proposed in this paper is that, the solution admits a exactly profile: $r^2 U(r)$ converges to some constant as $r$ goes to zero. In this talk, we mainly discuss how to solve this open problem when the domain is the whole space.

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