# PDE Seminar

## Report on Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system, I

### 白学利 博士 (华师大PDE中心博士后)

#### 2012年5月18日(周五)下午 1:00-2:50 闵行校区行政楼12楼PDE中心1202报告厅

Abstract. In this talk, I would like to introduce the main result of the paper ''Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system" which is written by Michael Winkler.

We consider the Neumann initial-boundary value problem for the following fully parabolic Keller-Segel system

\begin{equation}\left\{

\begin{array}{ll}

u_t=\Delta u-{\bf div} (u\nabla v), &x\in\Omega,t>0,\\[6pt]

v_t=\Delta v-v+u,&x\in\Omega,t>0.

\end{array}\right.

\end{equation}

where $\Omega$ is a ball in $\mathbb{R}^n$ with $n\ge 3$.

In this talk, I will prove that if the initial data $(u_0,v_0)$ belongs to some given set $S$, the energy will blow up in finite time, and hence the solutions blow up in finite time.