会议日程

一、活动时间：

2019年12月12日报到；

2019年12月13日学术报告；

2019年12月14日自由讨论。

二、活动内容：

1. 非线性偏微分方程及其应用领域的学术报告及交流；

2. 自由讨论。

三、报到和住宿：

南京市江宁区水秀苑大酒店（佳湖西路11号）

四、联系人：

李玉祥 联系电话：13770673528

李慧玲 联系电话：13505154693

吕小俊 联系电话：13813980592

马红铝 联系电话：13814087226

王小六 联系电话：15195929397

钟思佳 联系电话：13815855817

周春晖 联系电话：13512529021

研讨会日程表

12月12日下午：注册地点：水秀苑酒店 一楼大厅

晚餐：水秀苑酒店

12月13日： 东南大学数学学院第二报告厅

12月14日：自由讨论

题目和摘要

Design and analysis of SEIQR worm propagation model

in mobile internet

窦昌胜

首都经济贸易大学

The mobile Internet has considerably facilitated daily life in recent years. However, it has become the breeding ground for lots of new worms, including the Bluetooth-based worm, the SMS/MMS-based worm and the Wi-Fi-based worm. At present, Wi-Fi is widely used for mobile devices to connect to the Internet. But it exposes these devices to the dangerous environment. Most current worm propagation models aim to solve the problems of computer worms. They cannot be used directly in the mobile environment, particularly in the Wi-Fi scenario, because of the differences between computers and mobile devices. In this paper, we propose a worm propagation model in the Wi-Fi environment, called SEIQR (Susceptible-Exposed-Infectious- Quarantined-Recovered). In the model, infected nodes can be quarantined by the Wi-Fi base station, and a new state named the Quarantined state ( Q ) is established to represent these infected nodes. Based on this model, we present an effective method to inhibit the spread of the Wi-Fi-based worms. Furthermore, related stabilities of the worm-free and endemic equilibriums are studied based on the basic reproduction number R0. The worm-free equilibrium is locally and globally asymptotically stable if R0 < 1, whereas the endemic equilibrium is locally asymptotically stable ifR0 < 1. Finally, we evaluate the performance of our model by comprehensive experiments with different infection rates and quarantine rates. The results indicate that our mechanism can combat the worms propagated via Wi −Fi.

Some recent studies on Micropolar fluids.

段然

华中师范大学

Micropolar fluids are fluids with microstructure.Compared with traditional Navier-Stokes equations, there are extra terms standing for micro rotations which provide both damping terms and high nonlinear terms at the same time. Here we are going to introduce some of our recent studies on this model including existence of solutions to the initial boundary value problem and different kinds of large time behaviours.

Global weak solutions to the three-dimensional compressible non-Newtonian fluid

郭真华

西北大学

The equations of the three-dimensional compressible fluids with nonlinear constitutive equations are considered in a bounded domain. A solution to the initial-boundary value problem is constructed through an approximation scheme and a weak convergence method. The existence of a global variational weak solution to the three-dimensional equations of a compressible non-Newtonian fluid with large data is established.

Global well-posedness for the thermally radiative magneto hydrodynamics equations in 3D

蒋鹏

河海大学

Abstract: In this talk we study the thermally radiative magneto hydrodynamics equations in 3D, which describe the compressible viscous, heat-conducting fluid coupled with the Maxwell equations governing the behaviour of the magnetic field with taking into account the radiation effect under the non-local thermal equilibrium case. By using exquisite energy estimate, global existence and uniqueness of classical solutions to Cauchy problem in $\R^{3}$ or $\mathbb{T}^{3}$ is established when initial data is a small perturbation of some given equilibrium. The algebraic rate of convergence of solution toward the equilibrium state in $\R^{3}$ and exponential in $\mathbb{T}^{3}$, are also obtained under some additional conditions on initial data. The proof is based on Fourier multiplier technique.

Incompressible limit for the compressible Ericksen-Leslie's  hyperbolic liquid crystal model

栗付才

南京大学

In this talk, I shall discuss  the incompressible limit of the Ericksen-Leslie's hyperbolic liquid crystal model in compressible flow. We first derive the uniform energy estimates on the Mach number for both the compressible system and its differential system with respect to time under the uniformly in small initial data. Then, we take the limit in the compressible system to establish the global classical solution of the incompressible system. Moreover, we also obtain the convergence rates for the well-prepared initial data case.  This talk bases on the joint work with L. Guo, N. Jiang, Y. Luo and S. Tang.

Homogenization of Stokes equations in perforated domains: a unified approach

吕勇

南京大学

We consider the homogenization of the Stokes equations in a domain perforated with a large number of small holes which are periodically distributed. G. Allaire gave a systematic study on this problem. In this paper, we introduce a unified proof for different sizes of holes for the homogenization of the Stokes equations by employing a generalized cell problem inspired by L. Tartar.

Global well-posedness on the 3D incompressible Navier-Stokes and Euler equations in orthogonal curvilinear coordinate systems

王术

北京工业大学应用数理学院

We investigates the globally dynamical stabilizing effects of the geometry of the domain at which the flow locates and of the geometry structure of the solutions with the finite energy to the 3D incompressible Navier-Stokes and Euler systems. Under the suitable assumption on G. Lame coefficients, we establish the global well-posedness of the Cauchy problem for the 3D incompressible Navier-Stokes and Euler equations for a new class of the smooth large initial data in orthogonal curvilinear coordinate systems. Moreover, we also establish the existence, uniqueness and exponentially decay rate in time of the global smooth solution to the initial boundary value problem for the 3D Navier-Stokes equations for a class of the smooth large initial data and a large class of the special domain in orthogonal curvilinear coordinate systems. As its application, the corresponding results on the 3D incompressible Navier-Stokes and Euler equations in spherical coordinates are also given. Moreover, the related problems on the axisymmetric Navier-Stokes equations are surveyed and some results on the singularity formation and global regularity of an axisymmetric model for the 3D incompressible Euler and Navier-Stokes equations will also be reviewed.

Some recent progress on mathematical analysis

of a two-fluid type model

温焕尧

华南理工大学

In this talk, I will introduce three ways from different physical background how to derive a two-fluid type model. Then I will show some main challenges for associated problems, and introduce some recent results.

Local energy estimates and global solvability in a 3Dchemotaxis-fluid system with prescribed signal on the boundary

向昭银

电子科技大学

Base on the observation that the previous-used homogenous Neumann boundary is not successful in explaining pattern formation near the boundary, we deal with the chemotaxis-fluid system with signal consumption under the prescribed signal on the boundary.The main results assert that an associated initial-boundary value problem possesses a globally defined generalized solution. The analysis is based on a local energy estimation method which is quite unusual in the context of chemotaxis.

交通指南

1. 打车：南京南站至水秀苑酒店价格约25元；

   南京禄口机场至水秀苑酒店价格约85元。

2. 地铁：

   南京南站出发乘坐地铁1号线至百家湖站下，然后步行约1公里。

   禄口机场出发推荐打车。

     

与会人员

东南大学数学学院简介

东南大学数学学院始于1921年。当年著名数学家熊庆来先生从欧洲学成回国，于同年秋创立东南大学算学系，并任系主任。1952年院系调整后，从基础科学系，数学力学系，应用数学系直至发展为今天以教学科研并重、多学科全面发展、师资力量雄厚的数学学院。

学院下设基础数学系、应用数学系、计算数学系、系统科学系、统计与精算系和大学数学教学研究中心，以及江苏省网络群体智能重点实验室、无障碍联合重点实验室、丘成桐中心、数学研究所、应用数学研究所、应用概率统计研究所、金融统计研究所、复杂系统与网络科学研究中心、交通感知与认知研究中心、复杂系统协同控制实验室等多个教研机构。学院拥有数学博士后流动站，数学和网络空间安全（共享）2个一级学科博士点，数学与统计学2个一级学科硕士点，应用统计专业学位硕士点，数学和统计学江苏省重点学科，江苏省统计科研基地，江苏省“青蓝工程”科研创新团队，江苏省高等学校优秀教学团队和江苏省企业研究生工作站。学院拥有三个数学本科专业，与理学相关专业实行大类招生，大一共同培养，大二专业分流。数学与应用数学专业于2011年入选国家特色专业，是江苏省的特色专业、品牌专业。信息与计算科学专业于2008年被评为江苏省特色专业建设点。统计学和上述两个本科专业于2012年同时入选江苏重点专业类建设

一直以来，学院坚持基础研究与交叉应用并重，在数学以及相关交叉学科，特别是在复杂网络系统、群体智能、介质成像的科学计算、统计等领域开展了卓有成效的研究工作。近五年以来，我院数学学科ESI论文排名持续进入全国前10名，目前位列全球第86名、全国高校第8名。学院主持国家自然科学基金(重点、重大、面上、青年等) 60余项，多项研究成果获奖，其中包括首届全国创新争先奖1项、国家自然科学二等奖2项（参与）、江苏省科学技术一等奖1项、教育部自然科学二等奖3项、国家一级学会科学技术一等奖1项、汤森路透(Thomson Reuters)卓越研究奖1项、国家统计局优秀科技成果一等奖1项和二等奖2项、江苏省科学技术奖二等奖1项、三等奖2项。复杂网络团队引领国际潮流，“网络群体智能”入选东南大学十大科学问题，学科带头人应邀出席2018世界人工智能大会并发表主题演讲。

全院共有教职工110人，其中教授26人（校首席教授1人、校特聘教授1人、青年首席教授1人和青年特聘教授2人），副教授40人，讲师36人；博导21人、硕导54人。教师队伍中有欧洲科学院院士1人，欧洲科学与艺术院院士1人、巴基斯坦科学院院士1人，国际系统与控制科学院院士1人，IEEE Fellow 1人、汤森路透(Thomson Reuters)／科睿唯安(Clarivate Analytics)全球高被引科学家5人、首届全国创新争先奖获得者1人、爱思唯尔(Elsevier)中国高被引学者4人、教育部高等学校数学类专业和大学数学课程教指委各1人， 国家自然科学基金学科评审组专家1人、长江奖励计划青年学者1人、国家万人计划“青年拔尖人才”1人、国家青年千人1人、江苏省“333高层次人才培养工程”领军人才1人、国家优秀青年基金获得者2人、中国青年女科学家奖获得者1人、教育部高校青年教师奖获得者1人、教育部新世纪优秀人才支持计划3人、宝钢优秀教师特等奖提名奖获得者1人 、宝钢教育基金会优秀教师奖4人、霍英东青年教师基金资助获得者1人、德国洪堡基金资助获得者2人、江苏省双创人才2人、江苏省“六大人才高峰”4人、江苏省杰出青年科学基金获得者2人、江苏省优秀青年科学基金获得者1人、江苏省高校“青蓝工程”学术带头人4人等一大批科研精英和教学能手。同时，数学学院拥有一批具有世界一流学术水平的客座教授和产业教授，包括欧洲科学院院士1人，第三世界科学院院士1人，IEEE Fellow 2人。

学生培养成效显著，在各类奖项评比中表现优异，近五年来获全国百篇优秀博士学位论文提名奖1项，教育部博士研究生学术新人奖1项，江苏省优秀博士论文奖3篇，江苏省优秀硕士论文奖3篇，中国百篇最具影响国际学术论文奖2项、全国大学生“挑战杯”二等奖2项等一系列高水平奖励。毕业系友在国内外科学研究、企业创业等领域表现突出。杰出系友有程崇庆（长江学者特聘教授，国家杰青获得者）、吉敏（国家杰青获得者）、姚琦伟（著名统计学家）、郑维新（IEEE Fellow）、于敦德(途牛网CEO)等一批学术精英和业界翘楚。

学院为全校公共数学课程提供高水平的教学。“高等数学”、“数学建模与数学实验”、“线性代数与解析几何”三门公共基础课程相继被评为国家级精品课程、国家资源共享课程，同时“线性代数”入选中国大学MOOC。公共数学课程的教学团队被评为江苏省高等学校优秀教学团队，并获两项江苏省教学成果奖等一系列奖励。近年来，在数学学院教练团队指导下，东南大学数模竞赛成绩优异。2014年我校获国际大学生数模竞赛特等奖2项，位列国内第二。2016年，我校获全国大学生数模竞赛国家级一等奖4项，捧得本届竞赛最高奖“高教杯”。