主办单位：中国人民大学数学科学研究院

会议资助：国家自然科学基金

中国人民大学“双一流”基金

2021人民大学偏微方程系列报告会3

日程安排

2021年10月10日，周日，上午
腾讯会议ID：545 548 199
时间	会议内容
8:50-9:30	王克磊（武汉大学）
9:30-10:10	郑孝信（北京航空航天大学）
10:10-10:20	休息
10:20-11:00	杨文（中科院密测量科学与技术创新研究院）
11:00-11:40	季善明（华南理工大学）

《2021偏微方程系列报告会3》

报告题目与摘要

Asymptotic stability of solutions to a hyperbolic-ellipticcoupled system of the radiating gas on the half line

季善明

华南理工大学

报告摘要：This talk is concerned with the asymptotic stability of the solution to an initial-boundary value problem on the half line for a hyperbolic-elliptic coupled system of the radiating gas, where the data on the boundary and at the far field state are defined asu_-<u_+.For the scalar viscous conservation law case, it is known by the work of Liu, Matsumura, and Nishihara (SIAM J. Math. Anal.1998) that the solution tends toward rarefaction wave or stationary solution or superposition of these two kind of waves depending on the distribution of u_\pm. Motivated by their work, we prove the stability of the above three types of wave patterns for the hyperbolic-elliptic coupled system of the radiating gas with small perturbation.A singular phase plane analysis method is introduced to show the existence and the precise asymptotic behavior of the stationary solution, especially for the degenerate case: u_-<u_+=""0"" such that the system has inevitable singularities.The stability of rarefaction wave, stationary solution, and their superposition, is proved by applying the standard L^2-energy method.This is a joint work with Minyi Zhang and Changjiang Zhu.

演讲人简介：季善明，华南理工大学 副教授。主要研究方向为偏微分方程。目前已在Calc. Var. Partial Differential Equations, Nonlinearity, J. Differential Equations等杂志发表论文二十余篇。主持国家自然科学基金青年基金项目、中国博士后科学基金面上项目(一等)、广东省自然科学基金面上项目等。

Blow up analysis for Keller-Segel system

王克磊

武汉大学

报告摘要：In the Keller-Segel system describing chemotaxis, the solution may blow up in finite time. The blow up is caused by mass concentration. In this talk we will discuss a blow up analysis for this concentration phenomena. This is the first step to understand the blow up mechanism in the Keller-Segel system. This is a joint work with Chen Hua and Li Jian-Meng.

演讲人简介：王克磊，武汉大学，数学与统计学院教授。

On the uniqueness of equilibria in the Keller-Segel model

杨文

中国科学院精密测量科学与技术创新研究院

报告摘要：In this talk, we study the uniqueness of a semilinear elliptic equation with Dirichlet and Neumann boundary conditions, the equation arises as the stationary problem of the well-known classical Keller-Segel model describing chemotaxis. As a consequence of the uniqueness, we derive some results on the exact asymptotic behavior of solutions to the classical Keller-Segel system with subcrtical mass in two dimensions.

演讲人简介：杨文, 2015年获得加拿大英属哥伦比亚大学数学专业哲学博士学位，2015-2018年，先后在台湾大学理论科学研究中心以及香港理工大学从事博士后的研究工作。2018年2月在中科院武汉物理与数学研究所数学物理与应用研究部开始工作，任职副研究员。2019年4月任中科院武汉物理与数学研究所研究员。主要从事非线性椭圆型偏微分方程的研究，已在Arch.Rat.Mech.Anal,Int.Math.Res.Not.,J.Math.Pure.App.,Analysis&PDE,Comm.PDEs,Calc.PDE等国际数学期刊上正式和接受发表论文30余篇。

Large self-similar solutions to the generalized Naiver-Stokes equations

郑孝信

北京航空航天大学

报告摘要：We investigate regularity for weak solutions of the following generalized Leray equations which arises from the study of self-similar solutions to the generalized Naiver-Stokes equations in R^3.By developing non-local effects of the fractional diffusion operator, we prove uniform estimates for weak solutions in the weighted Hilbert space. This regularity result enables us to establish the self-similar solution to the Naiver-Stokes equations. Afterwards, we consider large self-similar solutions to convection-diffusion equation.

演讲人简介：郑孝信，任职于北京航空航天大学数学科学学院，博士毕业于中国工程物理研究院，波兰Wroclaw University大学博士后。 研究方向：调和分析、Navier-Stokes、SQG、Boussinesq、chemotaxis-Navier-Stokes等流体动力学方程。主持了2项国家自然科学基金项， 在 Adv. Math.、 Arch. Ration. Mech. Anal.、 Comm. Math. Phys.、 Transactions of the AMS、J. Math. Pures Appl.、SIAM J. Math. Anal.、 J. Differential Equations 等著名期刊上发表SCI论文20余篇。