主办单位： 中国人民大学数学科学研究院/数学学院

2022春季人民大学偏微方程小型研讨会II

日程安排

《2022春季人民大学偏微方程小型研讨会2》

报告题目与摘要

自食、扩散和交错扩散

伏升茂

西北师范大学

报告摘要：主要介绍自食、线性自扩散、分数型交错扩散和食饵趋向对捕食者-食饵阶段结构模型动力学性态的影响。

演讲人简介：伏升茂，现任西北师范大学数学与统计学院教授、博士研究生导师、中国生物数学学会常务理事。主要研究方向为偏微分方程与生物数学，共撰写和发表论文80余篇。主持完成4项、参与完成6项国家自然科学基金。曾获西北师范大学教学名师奖等。

On Keller-Segel-type systems with signal-dependent motilities

陶有山

上海交通大学

报告摘要：This lecture begins with briefly reviewing some boundedness and blow-up results on the Keller-Segel-production systems with signal-density suppressed motilities. Then, this talk reports a recent co-work, with Michael Winkler (Paderborn), on global weak solvability for a Keller-Segel-consumption system involving singularly signal-dependent motilities.

演讲人简介：陶有山，上海交通大学数学科学学院特聘教授。曾先后于南京大学、复旦大学、苏州大学分别获得数学学士、硕士和博士学位。主要研究方向为偏微分方程，特别是趋化交叉扩散方程，已在JEMS, PLMS, JFA, ANIHPC, SIMA, SIAP, Inverse Problems等国际数学期刊上发表论文90余篇，MR引用3400余次；2018-2021年连续四年入选科睿唯安“全球高被引科学家”； 现担任2份国际期刊Nonlinear Analysis: RWA和EMS Surveys in Mathematical Sciences的编委。

Aggregation-diffusion equation: symmetry, uniqueness and non-uniqueness of steady states

姚 珧

新加坡国立大学

报告摘要：The aggregation-diffusion equation is a nonlocal PDE that arises in the collective motion of cells. Mathematically, it is driven by two competing effects: local repulsion modeled by nonlinear diffusion, and long-range attraction modeled by nonlocal interaction. In this talk, I will discuss several qualitative properties of its steady states and dynamical solutions. Using continuous Steiner symmetrization techniques, we show that all steady states are radially symmetric up to a translation. (joint work with Carrillo, Hittmeir and Volzone). Once the symmetry is known, we further investigate whether steady states are unique within the radial class, and show that for a given mass, the uniqueness/non-uniqueness of steady states is determined by the power of the degenerate diffusion, with the critical power being m = 2. (joint work with Delgadino and Yan).

演讲人简介：Yao Yao is currently an Associate Professor of Mathematics at the National University of Singapore. She received her BS degree from Peking University in 2007, and PhD degree in 2012 from UCLA. She was a Van Vleck Visiting Assistant Professor at University of Wisconsin-Madison in 2012-2015, and an Assistant Professor at Georgia Institute of Technology in 2015-2021. Her research focuses on the analysis of partial differential equations arising in mathematical biology and fluid dynamics, especially on the equations with a nonlocal transport term. She was a recipient of the NSF CAREER Award in 2018 and Sloan Research Fellowship in 2020.

Global existence and boundedness for some chemotaxis models

闫建璐

南京航空航天大学

报告摘要： In this talk, we consider four types of chemotaxis models in biomathematics, which describes the directional movement of cells in response to the concentration gradient of a diffusible chemical signal. These four models are Keller-Segel systems, with nonlinear diffusion and singular sensitivity, heterogeneous Logistic sources, gradient-dependent chemotaxis sensitivity as well as p-Laplacian diffusion and gradient dependent chemotactic sensitivity, respectively. This talk is devoted to studying the global existence and boundedness of weak or generalized solutions for these chemotaxis models.

演讲人简介：闫建璐，南京航空航天大学讲师。2021年毕业于东南大学，同年获得理学博士学位。2019年9月-2020年9月受国家留学基金委资助在德国帕德伯恩大学交流学习。主要研究方向为偏微分方程，特别是Keller-Segel模型，发表SCI论文3篇，主持江苏省青年基金1项。