报告时间：2026年9月28日（星期一）10:30-11:30

报告地点：科教楼B座1710会议室

报  告  人：王炜 副研究员

工作单位：南京航空航天大学

举办单位：数学学院

报告简介：

This paper studies a stochastic version of the classical Keller--Segel (KS) system under homogeneous Neumann boundary conditions in a bounded two-dimensional domain O. The system we consider is

\begin{align*}

du - (r_u \Delta u- \chi \Div( u\nabla v)-\delta |u|^{q-1}u ) dt = u\circ dW_1, \\

dv - (r_v \Delta v -\alpha v) dt = \beta u dt+ v\circ dW_2,

\end{align*}

with initial condition $(u_0,v_0)$ on a filtered probability space $\mathfrak{A}$ and $W$ is a time-homogeneous spatial Wiener process with $\sigma$ being the noise coefficient. Here $u$ and $v$ denote the cell density and the concentration of the chemical signal, respectively. The positive terms $r_u$ and $r_v$ are the diffusivity of the cells and chemoattractant, respectively, the positive value is the diffusivity of the cells, $\chi$ is the chemotactic sensitivity, $\alpha\ge0$ is the so-called damping constant, $\beta\ge0$ is the production weight corresponding to $u$.Since the influence of random disturbance in demonstrating the mechanism of cell $u$ is intrinsic, the stochastic integral is interpreted in the Stratonovich sense. We will prove the existence of a unique local mild solution. The solvability is attained by first truncating the nonlinearity and showing the existence of the solution by the Banach Fixed Point Theorem. Secondly, we introduce a stopping time and establish some uniform bounds of the solution until the stopping time. In this way, we can extend in a final step the solution until the stopping time.

报告人简介：

王炜，南京航空航天大学数学学院副研究员，博士毕业于中国科学技术大学。主要研究方向为随机分析与随机偏微分方程，论文发表于J. Differ. Equ., Commun. Pure Appl. Anal., J. Theoret. Probab.等期刊。