## 応用解析セミナー

開催情報 木曜日　16:00～17:30　数理科学研究科棟(駒場) 002号室 石毛 和弘

### 2023年04月06日(木)

16:00-17:30   数理科学研究科棟(駒場) 126号室

Van Tien Nguyen 氏 (National Taiwan University)
Blowup solutions to the Keller-Segel system (English)
[ 講演概要 ]
I will present constructive examples of finite-time blowup solutions to the Keller-Segel system in $\mathbb{R}^d$. For $d = 2$ ($L^1$-critical), there are finite time blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized according to a discrete spectrum of a linearized operator around the rescaled stationary solution in the self-similar setting. There is a stable blowup mechanism which is expected to be generic among others. For $d \geq 3$ ($L^1$-supercritical), we construct finite time blowup solutions that are completely unrelated to the self-similar scale, in particular, they are of Type II with finite mass. Interestingly, the radial blowup profile is linked to the traveling-wave of the 1D viscous Burgers equation. Our constructed solution actually has the form of collapsing-ring which consists of an imploding, smoothed-out shock wave moving towards the origin to form a Dirac mass at the singularity. I will also discuss other blowup patterns that possibly occur in the cases $d = 2,3,4$.
[ 参考URL ]
https://forms.gle/7ogZKyh1oXKkPbN56