Special Session 1: Analysis of parabolic models for chemotaxis
Asymptotic profile to the blow-up solutions of parabolic-elliptic Keller-Segel-Patlak system in $\mathbb{R}^N$ with $N\ge 3$.
Xueli Bai
Northwestern Polytechnical University
Peoples Rep of China
Co-Author(s):    Maolin Zhou
Abstract:
In this talk, we obtained the exact blow-up profiles of solutions of the Keller-Segel-Patlak system in the whole space with dimensions $N\ge 3$ which partially solves an open problem proposed by P. Souplet and M. Winkler in [Souplet, Winkler, CMP, 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.
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