학술논문
Exact blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions $N\ge 3$
Document Type
Working Paper
Author
Source
Subject
Language
Abstract
In this paper, we obtain the exact blow-up profiles of solutions of the Keller-Segel-Patlak system in the space with dimensions $N\ge 3$, which solves an open problem proposed by P. Souplet and M. Winkler in 2019. To establish this achievement, we develop the zero number argument for nonlinear equations with unbounded coefficients and construct a family of auxiliary backward self-similar solutions through nontrivial ODE analysis.