*主持人：叶东 教授

*讲座内容简介：
In this talk, we first introduce geometric quantities for capillary hypersurfaces, and then establish isoperimetric type inequalities, Alexandrov-Fenchel inequalities, by studying corresponding geometric flows. We will also talk about a related Minkowski type problem and other related problems. The talk is based on a joint work with Chao Xia...

*主持人：叶东 教授

*讲座内容简介：

While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice and the face centered cubic lattice are both commonly observed in three dimensions. A geometric variational problem motivated by the diblock copolymer theory consists of a short range interaction energy and a long range interaction energy. In...

*主持人：叶东 教授

*讲座内容简介：

We prove that for $n=4$ and $6$, axially symmetric solution to the $\mathbb{Q}$-curvature type problem
$$
\alpha P_n u + c_n \left(1 - \frac{e^{nu}}{\int_{S^n}e^{nu}} \right) = 0
$$
on $S^n$ must be constants, provided that $\frac{1}{2} \le \alpha \le 1$. This result is sharp. The proof is based on two ty...

*主持人：叶东 教授

*讲座内容简介：
This talk is devoted to Hardy inequalities with best constants on Riemannian-Finsler manifolds. I will present the idea how to establish such inequalities by means of curvature on non-compact manifolds as well as on compact manifolds.

*主讲人简介：
赵唯，华东理工大学数学系副教授，主要研究Riemannian-Finsler几何和不对称度...

Abstract： In this talk, we propose a systematic approach to find the first integrals and Darboux polynomials of nonlinear differential systems. As applications, some new Darboux polynomials of nonlinear models arising in physics, biology, engineering, and fluid mechanics are investigated by this approach. Particularly, a nonintegrable three-dimensional system with non-chaotic behaviors is introdu...

*主持人：叶东 教授

*讲座内容简介：

The asymptotics of scalar phase transition models in the limit of vanishing interface width have been widely studied over the past decades. We will talk about some analogous results on phase transition models with high dimensional energy wells such as the matrix-valued Allen-Cahn equation and the isotropic-nematic interface problem i...

*主持人：何小清 教授

*讲座内容简介：

In this talk, we consider a type of non-uniformly parabolic problem with nonlocal term. First the classification of the finite-time blow-up/global existence phenomena based on the associated energy functional and explicite expression of all nonnegative steady states are demonstrated. More importantly, we derive that any bounded so...

*主持人：何小清 教授

*讲座内容简介：

In this talk, we mainly study non-negative classical solutions to a Neumann initial-boundary value problem for a higher dimensional parabolic elliptic ODE minimal chemotaxis-haptotaxis system. We first show pure haptotaixs cannot induce any blow-up and pattern in any dimensions, showing negligibility of haptotaxis on boundedness. ...

*主持人：何小清 教授

*讲座内容简介：

This talk is concerned with the existence and further properties of propagation speeds of transition fronts for bistable reaction-diffusion equations in exterior domains and in some domains with multiple cylindrical branches. In exterior domains we show that all transition fronts propagate with the same global mean speed, which tur...

*主持人：袁海荣 教授

*讲座内容简介：
In this talk, the compressible non-isentropic Euler equations with combustion reaction are used as the model to study the stability of steady strong detonation waves in a two-dimensional straight duct with constant cross-section. We construct a special solution of strong detonation wave that only depends on the normal direction of the duct...

主持人：叶东 教授

报告内容简介：
In this talk, we discuss some recent results on Liouville type theorems for steady Navier-Stokes system in a slab with either no-slip boundary conditions or periodic boundary conditions. In particular, we showed that bounded axisymmetric solutions in a slab must be zero or constant. The proofs are based on Saint-Vernant type estimate, which ar...

*主持人：叶东 教授

*讲座内容简介：
Motivated by studies of axially symmetric stationary solutions of the Einstein vacuum equations in general relativity, we study singular harmonic maps from domains of the 3-dimensional Euclidean space to the hyperbolic plane, with bounded hyperbolic distance to extreme Kerr harmonic maps. We prove that every such harmonic map has a unique t...

华东师范大学研究生暑期学校
“2022微分动力系统的多尺度方法”通知

主办单位：华东师范大学数学科学学院、华东师范大学研究生院、上海市核心数学与实践重点实验室

协办单位：中国数学会奇摄动专业委员会

华东师范大学数学科学学院是我国核心数学高层次人才培养的重要基地，以其雄厚的教学科研实力而声誉远播，曾培养了大量动力系统和奇异摄动领域的人才。为了进一步加强研究...

*时间：2022年7月4日 19:30-20:30 2022年7月5日 19:30-20:30
*地点：腾讯会议：170-612-898 会议密码：220704
*主讲人：张大军 教授
*主持人：傅蔚 副教授

*讲座内容简介：
椭圆曲线与可积系统之间的交叉主要体现在用椭圆函数（或双周期函数）来刻画的精确解和可积方程的椭圆形变。前者例如代数几何解，后者指方程中的系数后某些项服从椭圆曲线。报告主要介绍基于Lamé函数的KP型方程...

*主持人：傅显隆 教授

*讲座内容简介：
In this talk, I will introduce a periodic discrete model to study the dynamics of Wolbachia infection frequency in mosquito populations where infected mosquitoes are impulsively released. This model has three notable characteristics: First, it covers all relevant existing models since 1959 as special cases. Second, it develops with the dev...

*主持人：叶东 教授/ 张艳艳 副教授

*讲座内容简介：
In this talk，I shall introduce a recent result on existence and upper semicontinuity of time-dependent attractors for the non-autonomous nonlocal diffusion equations. This work is jointly with Bin Yang.


*主讲人简介：

秦玉明，教授（2级）、博士生导师，复旦大学博士、巴西国家科技部国家科学计...

*主持人：傅显隆 教授

*讲座内容简介：
In this talk we introduce some results on the global and local integrability of systems of ordinary differential equations, and the methods used in the study of these problems. The main results are on Darboux and Liouville integrability of polynomial differential systems，and the existence and regularity of local first integrals near singu...

*主持人：傅显隆 教授

*讲座内容简介：
Since the independence of focal values is a sufficient condition to give a number of limit cycles arising from a center-focus equilibrium, in this paper we consider a restricted independence to a parametric curve, which gives a method not only to increase the lower bound for the cyclicity of the center-focus equilibrium but also to be avai...

*主持人：叶东 教授

*讲座内容简介：
We consider a semilinear elliptic equation in a smooth bounded domain. By using the minimax methods, bifurcation methods, Conley index theory and Morse theory, we obtain six nontrivial solutions for the equations with coercive nonlinearities. This is a joint work with Yutong Chen, Jiabao Su and Mingzheng Sun.

*主讲人简介：

*主持人：傅显隆 教授

*讲座内容简介：
This talk reports some recent progress in the study of a four-component haptotaxis model describing the process of oncolytic virotherapy, and it is based on several works cooperated with Michael Winkler (Paderborn). The presentation addresses global classical solvability, a critical mass phenomenon for infinite-time blow-up, a borderline v...

*主持人：傅显隆 教授

*讲座内容简介：
We study the dynamics of two-species competition model in advective, patch environment. Organisms can move between connected patches, and they are also subject to the passive, directed drift from “upper stream” patch to “down stream” patch. A complete understanding is given for the two-patch case. We will mainly discuss three-patch mod...

*主持人：叶东 教授

*讲座内容简介：
In this talk, we study a system of two coupled time-independent Gross-Pitaevskii equations, which is used to model two-component Bose-Einstein condensates with attractive interactions. For a certain type of trapping potentials, especially for the degenerate ring-shaped potentials, we investigate the existence, concentration and local uniquen...

*主持人：张艳艳 副教授

*讲座内容简介：
In the talk, a family of solutions of piecewise constant vorticity to several fluid systems will be introduced. The equations of the contour dynamics under different geometrical situations will be formulated. Those equations are usually nonlinear nonlocal dispersive equations. The global well-posedness of the solutions will be proved un...

*主持人：叶东 教授

*讲座内容简介：
In this talk I will first introduce some qualitative properties of the solutions of the critical Hartree equation, such as the regularity, symmetry, decay estimates, classification and nondegeneracy. Then as an application of the properties, we will apply variational methods and Lyapunov-Schmidt reduction arguments to study the existence, mu...

*主持人：袁海荣 教授

*讲座内容简介：
于慧敏，山东师范大学数学与统计学院教授、博导，山东师范大学东岳学者。2008年从中国科学院数学与系统科学研究院获理学博士学位，主要从事偏微分方程的理论与应用研究。在 SIAM J. Math. Anal.、 J. Differential Equations、 Commun. Math. Sci，Z. Angew. Math. Phys. 等国际期刊发表学术论文二十余篇， 一篇文章获首届《中国科学：数学》优秀论文提名奖。
...

*主持人：何小清 青年研究员

*讲座内容简介：
Incorporating time delay and Stefan type free boundary into reaction-diffusion equation yields a compatible condition, which guarantees the well-posedness of the initial value problem. Further, under a KPP type setting we establish a dichotomy on propagation or vanishing. When propagation happens, the spreading speed is shown to exis...

*主持人：叶东 教授

*讲座内容简介：
The so-called zero number diminishing property is a property on the solutions to one dimensional parabolic equation, which says that the number of the zeros of a certain solution is non-increasing in time. This property, developed by H. Matano, S. Angenent et al, is a powerful tool in studying the asymptotic behavior of the solutions. Recent...

*主持人：叶东 教授

*讲座内容简介：

自然界中的物质输运与流体运动有着密切的关系：通过流体的搅拌，这些物质传递的效率得到了提升；溶质浓度场在流体中的不均匀分布又往往会带来流体的对流运动。在本此报告中，我将介绍纽约大学应用数学实验室针对自然界中溶解问题的研究。在实验角度，我们通过小尺度实验室实验再现了自然界中岩石的演化、石林的形成等等地质现象。在数值角度，我们提出了一种高精...

*主持人：张静 副教授

*讲座内容简介：

辛扭转映射是正定拉格朗日变分研究最广泛的一类，在物理天文等现实问题上有深刻的应用。我们将对于这一客体的全局解的正则性以及奇性给出几何刻画，并用以解释diffusion现象的成因。

*主讲人简介：

张建路，南京大学数学系2005-2014本硕博连读，后陆续在多伦多大学，苏黎世eth，加州大学伯克利分校从事博士后研究工作，2019年入...

*主持人：叶东 教授

*讲座内容简介：
我们将讨论周期抛物算子主特征值对疾病空间传播的应用，例如确定时空异质环境中基本再生数对于多个参数的依赖关系，其中的一个出发点是基本再生数对于频率的单调性。

*主讲人简介：
楼元，美国俄亥俄州立大学、上海交通大学数学科学学院教授，博士生导师。1988年本科毕业于北京大学数学系;1991年硕士毕业于北京大学数学系;1995年博毕业于明尼苏达...

*主持人：叶东 教授

*讲座内容简介：

The classical Moser-Trudinger inequality is a borderline case of Soblolev inequalities and plays an important role in geometric analysis. Aubin in 1979 showed that the best constant in the Moser-Trudinger inequality can be improved by reducing to one half if the functions are restricted to the complement of a three dimensional subs...

*讲座内容简介：

This talk reports a recent progress in the study of so-called pursuit-evasion system which describes a fully cross-diffusive interaction mechanism between predators and preys. The system formally possesses two basic entropy-like structures, but the regularity thereby implied seems insufficient to ensure global solvability for large data. We design a suitable thin-fil...

*讲座内容简介：

本报告阐述学术论文写作前后需要关注的一些事项，包括研究生课程学习，毕业论文如何选题，如何进行课题研究，论文写作与修改，投稿和发表等。



*主讲人简介：

韩茂安，男，二级教授、博士生导师。曾获得国家中青年突出贡献专家称号、入选教育部新世纪优秀人才支持计划和上海市优秀学科带头人支持计划、获得宝钢优秀教师奖，曾作为第一完成人分别获得...

*讲座内容简介：

Classic criterion of asymptotic stability requires the condition of negative definiteness of the Liapunov function. In this talk we introduce some new weak criteria for asymptotic stability, which do not require the negative definiteness.



*主讲人简介：

张伟年教授，杰青，84年毕业于北京大学数学系，87年获中国科学院硕士，并于...

*讲座内容简介：

In this talk, we present the joint works with Professor Yuri Trakhinin on the local well-posedness of the free boundary problem in ideal compressible magnetohydrodynamics with or without surface tension. The Rayleigh-Taylor sign condition on the total pressure is required only for the case of zero surface tension.



*主讲人简介：
...

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In this talk, we will introduce the properties of positive solutions to some kinds of the elliptic equation in unbounded cylinder with zero boundary condition. After establishing an Aleksandrov-Bakelman-Pucci maximum principle in unbounded cylinder, the solution spaces can be classified. In particular, we will show that one solution spa...

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In this talk, we will discuss some weak dissipative systems, in which loss-regularity phenomenon will occur. Some methods are introduced to prove the local or global well-posedness of these dissipative systems in some weighted Sobolev Space.


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????????????????????????????????????2008?????...

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We investigate the nonexistence and existence of nontrivial positive solutions to

$\Delta_m u+u^p|\nabla u|^q\leq0$ on noncompact geodesically complete Riemannian manifolds, where $m>1$, and $(p,q)\in \mathbb{R}^2$.

According to a complete classification of $(p, q)$, we establish different volume growth con...

*主持人：叶东 教授

*讲座内容简介：

It is known that ground states of the pseudo-relativistic Boson stars exist if and only if the stellar mass N>0 satisfies N

*主持人：叶东 教授

*讲座内容简介：
We show Bernstein type results for entire self-shrinking solutions to Lagrangian mean curvature flow in . The proofs rely on a priori estimates and barriers construction. This is a joint work with Prof. Rongli Huang and Wenlong Wang.

*主讲人简介：
欧乾忠，广西师范大学数学与统计学院教授，分别于2004年、2008年硕士、博士毕...

*时间：2021年3月26日周五13:30-14:30
*地点：腾讯会议ID：928 821 274 链接：https://meeting.tencent.com/s/AGFZ4MYVMV3c
*主讲人：沈春 教授（鲁东大学）
*主持人：袁海荣 教授

*讲座内容简介：
The constructions of Riemann solutions for a second-order traffic flow model derived from a nonlinear Vlasov type kinetic model are displayed in fully explicit forms. In p...

*主办单位：数学科学学院
*举办形式：线上
*时间：2021年3月19日周五20:00-21:00
*地点：腾讯会议ID：431 397 045 链接：https://meeting.tencent.com/s/DZSt525IPNVg
*主讲人：陈青山 副教授 （美国克莱姆森大学Clemson University）
*主持人：袁海荣 教授

*报告内容简介：
Many critical applications, such as extreme weather forecast, rely on accurate simulati...

*主持人：何小清 青年研究员
*时间：2021年3月5日14:00-15:00
*地点：腾讯会议ID：325 178 798（https://meeting.tencent.com/s/ZMEisqkRm3oN）


*讲座内容简介：
Of concern is the Fisher-KPP equation on the xy-plane with an “effective boundary condition” imposed on the x-axis. This model, recently derived by Huicong Li and me, is meant to model the scenario of f...

*主持人：曹永罗 教授
*时间：2021年1月22日15：00-16:00
*地点：腾讯会议ID：951 579 554

*讲座内容简介：
It is well known that invariant torus with Diophantine frequnecy survives small perturbation, but the one with resonant frequency will be destructed by arbitrarily small perturbation. In this talk, I shall briefly review the result about the top...

主持人: 何小清 青年研究员
报告时间: 2021年1月15日上午8:30-9:30
报告平台: 腾讯会议 ID：112 240 158（https://meeting.tencent.com/s/daNQDcJvn3gk）
主办单位：数学科学学院、科技处

报告人介绍：King-Yeung Lam, 美国俄亥俄州立大学副教授。2011年于美国明尼苏达大学获得博士学位，师从倪维明教授。在美国俄亥俄州立大学(OSU)先后为Mathematical Biosciences Institute 博士后、Zassenh...

*主持人：何小清 青年研究员
*时间：2020年12月18日8:30-9:30
*地点：腾讯会议 房间号：547 586 910

*讲座内容简介：
We will first introduce a semi-linear parabolic system that describes the evolution of gene frequencies under the joint action of migration and selection. Then, we will report some recent progress made on the two-allele case with complete dominance...

*主持人：周风 教授
*时间：2020年12月11日13：30-14:30
*地点：腾讯会议ID：309 752 558


*讲座内容简介：

This talk is concerned with several types of nonlinear Schrodinger equations with differential potentials. We first discuss the variational characteristics for the time-independent Schrodinger equations. Then we establish the sharp con...

*主持人：周风 教授
*时间：2020年11月25日15:00-16:00
*地点：闵行校区数学楼102报告厅 + 腾讯会议 ID：770 528 272


*讲座内容简介：
具有牛顿势的多体问题来源于牛顿于1687年出版的巨著《自然哲学的数学原理》。自那以后，许 多著名的数学家,物理学家和天文学家受益于它,对于理解它做出了巨大的贡献，如Euler, Lagrange,Laplace, Hamilton,Jacobi，Poincaré Birkho...