第十届华东偏微分方程会议 - East China Normal University · 2015. 6. 9. · Masaharu Taniguchi(谷口雅治) Okayama University, Japan. In this talk I first survey recent

第十届华东偏微分方程会议 The Tenth East China Partial Differential Equations Conference

( June 15-18, 2015， CPDE, ECNU, Shanghai, China)

（图书馆一楼报告厅）

华东师范大学偏微分方程研究中心成立于 2010 年 9 月，是学校的实

体研究单位。偏微分方程中心致力于建设一个开放、活跃、富于创新的研

究平台，成为国内领先、国际一流的偏微分方程研究基地。在中心主任、

国家 "千人计划" 特聘教授倪维明的领导下，中心的工作已全面展开。在

中心成立四年多以来的时间里，已有百余位国内外偏微分方程领域的优秀

学者来华东师大访问交流。

"华东偏微分方程会议"之目的在于汇集国内外偏微分方程，特别是椭

圆/抛物型方程及相关学科的专家、学者共同介绍、研讨他们研究领域中的

新进展和新动向，并加强彼此之间的相互了解与合作。自 2004 年起，于

每年 7 月由华东师范大学数学系协同国内其它数学院系，分别在南京大学

(2004 年、2008 年)、华东师范大学 (2005 年、2006 年、2009 年)、烟台

大学 (2007 年)、华中师范大学 (2010 年)、陕西师范大学 (2011 年)、山

西大学 (2012 年) 已经成功的举办了九届该系列会议。

此次会议于 2015 年 6 月 15 日至 6 月 18 日在华东师范大学举办，

2015 年也适逢“Journal of Differential Equations (微分方程杂志)”创刊

50 周年，Elsevier 出版社将藉此次华东偏微分方程会议庆祝这一里程碑；

同时为第一届 Hale Award 获奖人 Bjorn Sandstede （Brown University）

颁奖。届时，当前的四位主编：Alberto Bressan、周修义(Shui-Nee Chow)、

John Mallet-Paret、以及倪维明 (Wei-Ming Ni)，都将出席。邀请与会的

有数位编委，包括：包刚 (Gang Bao)、楼元 (Yuan Lou)、魏军城

(Juncheng Wei) 等，将全程参会。此外，Hale Award Lecture 也将安排

在会议的第一天议程之中。

丁伟岳院士于 2014 年 11 月 11 日不幸逝世。丁伟岳院士生前一直是

我国数学发展的积极推动者，也是华东偏微分方程会议始终如一的支持者。

我们十分怀念这位杰出的数学家和老朋友。

学术委员会

倪维明（主席华东师范大学，University of Minnesota, USA）

张恭庆（北京大学）

丁伟岳（北京大学、中国科学院数学所）

洪家兴（复旦大学）

姜礼尚（同济大学）

李大潜（复旦大学）

林芳华（Courant Institute， New York University, USA）

潘兴斌（华东师范大学）

尤建功（南京大学）

尹会成（南京师范大学）

辛周平（香港中文大学）

组织委员会

周风（主席华东师范大学）李芳（华东师范大学）

王丽萍 (华东师范大学) 赵纯奕 (华东师范大学)

谢宇（华东师范大学）

会议报到

会议将于 2015年 6月 14日上午 9:00至下午 6:00在沪华酒店和海舟酒店一

楼接待大厅办理报到手续。

会议地点

华东师范大学闵行校区图书馆一楼报告厅。

入口：图书馆一楼单独开通了会场入口，届时会有会议宣传海报作为方向指引。

会议期间，请不要上二楼进入图书馆主楼的资料借阅区。

住宿地址

会议期间，注册人员的早、中、晚餐，可凭报到时领到的饭票在学校华闵食

堂一楼会议专窗用餐（见地图），18日的早、中餐在公共窗口用餐。

除有特殊要求外，为参会人员预订的住宿信息已经发送给各位，请根据自己

的入住预订办理手续，地址供参考：

沪华酒店：闵行区剑川路 368号，298元起，021-64509777；

海舟酒店：虹梅南路 5688号，260元，021-54399055；

教师之家宾馆：虹梅南路 5858号，238 元，021-33503666。

联系信息

联系人：谢宇（华东师范大学）李芳（华东师范大学）

通信地址：上海市闵行区东川路 500号华东师范大学偏微分方程中心

邮编：200241 电话： 021-54343074 手机：15021016064

Email：[email protected]；[email protected]

会议网址：http://www.cpde.ecnu.edu.cn/10thECPDE/

mailto:[email protected]:[email protected]://www.cpde.ecnu.edu.cn/10thECPDE/

第十届华东偏微分方程会议--The Tenth East China Partial Differential Equations Conference

June 15

June 16 June 17 June 18

Mo

rnin

g S

es

sio

n

09:00-09:10 开幕式

(Opening Ceremony)

09:10-10:00 Bjorn Sandstede

(Hale Award Lecture)

09:30-10:20 林芳华

(Fanghua Lin)

汪徐家

(Xujia Wang)

张旭

(Xu Zhang) 10:00-10:20 照相 (Group Photo)

10:20-10:50 Tea/Coffee Break 10:20-10:50 Tea/Coffee Break

10:50-11:40 包刚

(Gang Bao) 10:50-11:40

魏军城

(Juncheng Wei)

任晓峰

(Xiaofeng Ren)

何小清

(Xiaoqing He)

Lunch Break

Aft

ern

oo

n S

es

sio

n 02:00-02:50 楼元

(Yuan Lou) 02:00-02:50

陈俊全

(Chiun-Chuan Chen)

潘兴斌

(Xingbin Pan)

03:00-03:50 Masaharu Taniguchi

(谷口雅治) 03:00-03:50

尤建功

(Jiangong You)

陈文雄

(Wenxiong Chen)

03:50-04:20 Tea/Coffee Break 03:50-04:20 Tea/Coffee Break

04:20-05:10 麻希南

(Xinan Ma) 04:20-05:10

彭锐

(Rui Peng)

王学锋

(Xuefeng Wang)

Dinner

Day 1: June 15, Monday

Morning Session

09:00-09:10 (Opening Ceremony)

09:10-10:00 Bjorn Sandstede (Hale Award Lecture)

Defects: Classification, Existence, and Stability

10:00-10:20 (Group Photo)

10:20-10:50 Tea/Coffee Break

10:50-11:40 (Gang Bao)

Recent Studies of Inverse Scattering Problems

11:40-14:00

Afternoon Session

14:00-14:50 (Yuan Lou)

Cross-Diffusion Models in Population Dynamics

15:00-15:50

Masaharu Taniguchi( )

Multidimensional Traveling Fronts in Reaction-Diffusion

Equations


16:20-17:10

(Xinan Ma)

The Convexity of the Solution for Elliptic and Parabolic Partial

Differential Equations

17:10-18:30

Day 2: June 16, Tuesday

Morning Session

09:30-10:20 (Fanghua Lin)

Extremum Problems for Laplacian Eigenvalues


10:50-11:40 (Juncheng Wei)

On Secondary Reduction Method and Applications

11:40-14:00

Afternoon Session

14:00-14:50 (Chiun-Chuan Chen)

Critical Exponent for A PDE Model of Spot Replication

15:00-15:50

(Jiangong You)

Problems Related to the Schrodinger Equation with Ergodic

Potential


16:20-17:10

(Rui Peng)

The Principle Eigenvalue for

Some Periodic-Parabolic Problems with Applications

17:10-18:30

Day 3: June 17, Wednesday

Morning Session

09:30-10:20 (Xujia Wang)

The p-Minkowski Problem


10:50-11:40

(Xiaofeng Ren)

The Impact of the Domain Boundary on an Inhibitory System:

Boundary Half Discs in Stationary Assemblies

11:40-14:00

Afternoon Session

14:00-14:50 (Xingbin Pan)

Regularity of Weak Solutions to Nonlinear Maxwell Systems

15:00-15:50

(Wenxiong Chen)

Direct Methods of Moving Planes, Moving Spheres,

and Blowing-Ups for the Fractional Laplacian


16:20-17:10

(Xuefeng Wang)

A (Biased) Survey on Elliptic,

Parabolic and Nonlocal Eigenvalue Problems

17:10-18:30

Day 4: June 18, Thursday

Morning Session

09:30-10:20 (Xu Zhang)

Transposition method for BSEEs and application


10:50-11:40

Xiaoqing He

Global Dynamics of Heterogeneous Lotka-Volterra Competition-

Diffusion Systems

11:40-14:00

End of THE Conference

Thank you very much for your attendance

Defects: Classification, Existence, and Stability

Bjorn Sandstede

Brown University, USA

Defects arise as solutions to partial differential equations: they can be thought of as

interfacial regions that mediate between different spatially periodic patterns. In this

talk, I will review the classification, existence, and nonlinear stability of defects in one

space dimension. The proofs utilize a combination of spatial dynamical systems

techniques and pointwise PDE estimates. I will also outline open problems in one and

two space dimensions.

Recent Studies of Inverse Scattering Problems

包刚(Gang Bao)

浙江大学

The inverse scattering problem arises in diverse areas of industrial and military

applications, such as nondestructive testing, seismic imaging, submarine detections,

near-field or subsurface imaging, near-field and nano optical imaging, and medical

imaging. The model problem is concerned with a time-harmonic electromagnetic

plane wave incident on a medium enclosed by a bounded domain. Given the incident

field, the direct problem is to determine the scattered field for the known scatterer.

The inverse scattering problem is to determine the scatterer from the boundary

measurements of near field currents densities. Although this is a classical problem in

mathematical physics, mathematical analysis and numerical solution of the inverse

problems remain to be challenging since the problems are nonlinear, large-scale, and

most of all ill-posed! The severe ill-posedness has thus far limited in many ways the

scope of inverse problem methods in practical applications.

In this talk, our recent progress in mathematical analysis and computational studies of

the inverse scattering problems will be reported. A novel stable continuation approach

based on the uncertainty principle will be presented. By using multi-frequency or

multi-spatial frequency boundary data, our approach is shown to overcome the ill-

posedness for the inverse scattering problems. New stability and uniqueness results

for the inverse problems will be presented. The speaker will also highlight ongoing and

future projects along these directions.

Cross-Diffusion Models in Population Dynamics

楼元(Yuan Lou)

中国人民大学、The Ohio State University, USA

Cross-diffusion system is an important class of reaction-diffusion problems. At the

individual level, the basic underlying assumption for cross-diffusion is that the

transition probability only depends upon departure conditions, e.g., population

density and environmental condition at the departure location. We will mainly discuss

the Shigesada-Kawasaki-Teromoto model for two competing species. This talk is based

on joint works with Wei-Ming Ni, Michael Winkler, Shoji Yotsutani.

Multidimensional Traveling Fronts in Reaction-

Diffusion Equations

Masaharu Taniguchi(谷口雅治)

Okayama University, Japan

In this talk I first survey recent studies on traveling waves in reaction-diffusion equation

(unbalanced Allen-Cahn equation, Fisher-KPP equation, combustion equation) and

cooperation-diffusion systems in multidimsional spaces. Finally I explain my recent

work on unbalanced Allen-Cahn equations and cooperation-diffusion systems. Let an

integer N be greater than 2. Let (N-2)-dimensional smooth surfaces be given as

boundaries of strictly convex compact sets in the (N-1)-dimensional space. I prove that

there exists a traveling front associated with a given surface and show its stability.

The Convexity of the Solution for Elliptic and

Parabolic Partial Differential Equations

麻希南(Xinan Ma)

中国科学技术大学数学科学学院

We study the convexity of the level sets for the solutions of elliptic and parabolic

partial differential equations. We shall first review the main techniques to get the

convexity of the solution or the level sets of the solutions. Then we concentrate on the

constant rank theorems which constitute an important tool to study convexity

properties of the solutions to elliptic and parabolic partial differential equations.

Especially we obtain a constant rank theorem for the second fundamental form of the

space-time level sets of a space-time quasiconcave solution of the heat equation. Then

we combine this constant rank theorem with a deformation process to get the spatial

and space-time quasi-concavity of the solution of the heat equation in a convex ring,

when the initial data is quasiconcave and subharmonic. We also mention some

qantitative results on the shape of the level sets of the solutions using the known data.

Extremum Problems for Laplacian Eigenvalues

林芳华(Fanghua Lin)

Courant Institute of NYU,USA

Eigenvalue Problems for Laplacians are among most well-known problems in classical

analysis, partial differential equations and calculus of variations. In this lecture I shall

discuss a couple very basic extremum problems involving eigenvalues of the Laplacian.

Such problems arise in shape optimizations, pattern formations ......, and solutions to

these problems have been challenging for a very long time. In particular, we shall see

how classical Rayleigh-Faber-Krahn inequalities, Weyl's asymptotic formula and Polya's

Conjecture, along with theorems concerning nodal domains coming into play in

understanding of these problems. The lecture would be a brief and elementary survey

of some of recent results.

On Secondary Reduction Method and

Applications

魏军城(Juncheng Wei)

The University of British Columbia, Canada

I will discuss improved secondary reduction method and its applications, including

(1) Optimal number of interior spike solutions for Lin-Ni-Takagi prolem

2 0 in , 0 onpu u u u

(2) Concentration on an open segment of the boundary for Lin-Ni-Takagi problem

(3) The existence of infinitely many positive solutions to

1( ) 0, 0 in ,p Nu V x u u u R u H

under non-symmetric potentialV .

Critical Exponent for A PDE Model of Spot

Replication

陈俊全(Chiun-Chuan Chen)

National Taiwan University

We proposed a simple PDE model which exhibits self-replication of spot solutions in

any dimension. This model was analyzed in one and higher dimensions. In the radially

symmetric case, we demonstrated that the non-existence of a ground state solution is

crucial for self-replication and the conditions proposed by Nishiura and Ueyama are

satisfied. In this talk, we further discuss the non-existence property of this model

without the assumption of radial symmetry and show that this property is related to a

critical Ding-Ni exponent of the nonlinear term in the model. This is a joint work with

Theodore Kolokolnikov and Li-Chang Hung.

Problems Related To the Schrodinger Equation

with Ergodic Potential

尤建功(Jiangong You)

南京大学数学系

Linear and nonlinear Schrodinger equations with ergodic potential, especially random

potential or quasi-periodic potential, have strong background quantum physics. We

are interested in the evolution of solutions with localized initial datum, for example, if

it is always localized? To study this kind of problems, one need to study the spectral

theory of the corresponding Schrodinger operators as well as some related problems

in dynamical systems. We will give a brief introduction to the subject and some of our

related works.

The Principle Eigenvalue for Some Periodic-

Parabolic Problems with Applications

彭锐(Rui Peng)

江苏师范大学

In this talk, I shall give a brief review on principal eigenvalues of the second-order

linear elliptic and periodic-parabolic problems. Then I shall report our recent research

on the qualitative analysis of the principal eigenvalue of periodic-parabolic equations.

I shall also present some applications of these results to problems arising from

population biology and epidemiology.

The p-Minkowski Problem

汪徐家(Xujia Wang)

Australian National University, Australia

The p-Minkowski problem is an extension of the classical Minkowski problem. It

concerns the existence, uniqueness, and regularity of closed convex hypersurfaces

with prescribed Gauss curvature. The Minkowski problem has been studied by many

people in the last century and has been completely resolved. The p-Minkowski

problem was introduced in 1990s and involves more applications.

To study the p-Minkowski problem, one is led to a Monge-Ampere equation on the

unit sphere, which is related to the Blaschke-Santalo inequality. The existence,

uniqueness, and regularity of solutions depend on the parameter p. For example for

one range of p we have the uniqueness of solutions and for another range of p we may

have infinitely many solutions. As one will see, the p-Minkowski shares many similar

properties as the semilinear elliptic equations on the sphere. In this talk we will review

the development of the study of the p-Minkowski problem and discuss some recent

works on the problem.

The Impact of the Domain Boundary on an

Inhibitory System: Boundary Half Discs in

Stationary Assemblies

任晓峰(Xiaofeng Ren)

The George Washington University, USA

The nonlocal geometric variational problem derived from the Ohta-Kawasaki diblock

copolymer theory is an inhibitory system with self-organizing properties. The system

can prevent a disc from drifting towards the domain boundary. This raises the question

whether a stationary set may have its interface touch the domain boundary. It is

proved that a small, perturbed half disc exists as a stable stationary set, where the

circular part of its boundary is inside the domain, as the interface, and the almost flat

part of its boundary coincides with part of the domain boundary. The location of the

half disc depends on two quantities: the curvature of the domain boundary, and a

remnant of the Green's function after one removes the fundamental solution and a

reflection of the fundamental solution. The notion of reflection here is an interesting

new concept that generalizes the familiar notions of mirror image and circle inversion.

Our analysis of a boundary half disc leads to constructions of stationary assemblies

with both interior discs and boundary half discs.

Regularity of Weak Solutions to Nonlinear

Maxwell Systems

潘兴斌(Xingbin Pan)

华东师范大学

We examine regularity of weak solutions of several nonlinear Maxwell systems by

using of the iteration method. This method reduces the original system into two div-

curl systems and an oblique derivative problem of a quasilinear elliptic equation, and

makes it possible to improve the regularity of the solutions by iteration. The iteration

method is also used to show existence of steady states of a thermoelectrical model.

Direct Methods of Moving Planes, Moving

Spheres, and Blowing-Ups for the Fractional

Laplacian

陈文雄(Wenxiong Chen)

Yeshiva University, USA

Many conventional approaches on partial differential operators do not work on the

nonlocal fractional operator. To overcome this difficulty arising from non-localness,

Caffarelli and Silvestre introduce the extension method to reduced the problem into a

local one in one higher dimensions, which has become a powerful tool in studying such

nonlocal problems and has yielded a series of fruitful results.

However, due to technical restrictions, sometimes one needs to impose extra

conditions when studying the extended problems in higher dimensions, and these

conditions may not be necessary if we investigate the original nonlocal problems

directly.

In this talk, we will introduce direct methods of moving planes, moving spheres, and

blowing-up and re-scaling arguments for the fractional Laplacian. By an elementary

approach, we will _rst show the key ingredients needed in the method of moving

planes either in a bounded domain or in the whole space, such as strong maximum

principles for anti-symmetric functions, narrow region principles, and decay at in_nity.

Then, using simple examples, semi-linear equations involving the fractional Laplacian,

we will illustrate how this new method of moving planes can be conveniently

employed to obtain symmetry and non-existence of positive solutions, under much

weaker conditions than in the previous literatures.

We firmly believe that these ideas and approaches can be effectively ap- plied to a

wide range of nonlinear problems involving fractional Laplacians or other nonlocal

operators.

A (Biased) Survey on Elliptic, Parabolic and

Nonlocal Eigenvalue Problems

王学锋(Xuefeng Wang)

Tulane University, USA

The literature on eigenvalue problems is vast and so I am forced to be focused and

biased in this survey talk. I will emphasize results that help to understand the strength

of diffusion, the long term behavior of the corresponding evolution equation, and

results that I perceive as directly useful for researchers who do nonlinear analysis such

as stability and bifurcation analysis. Topics will include characterizations of eigenvalues,

especially of the principal eigenvalue, of local and nonlocal operators, nodal property

and multiplicity, effect of domain geometry on the size of the first nontrivial eigenvalue

and shape optimization, effect of parameters such as diffusion and advection

coefficients, nonlinear Krein-Rutman theory and its consequences to nonlinear

systems. Through out the talk, I will mention open problems, some of which are well-

known and long-standing, others new.

Transposition Method for BSEEs and

Application

张旭(Xu Zhang)

四川大学

Stimulated by the classical transposition method in PDEs, we introduced a new notion

of solution, i.e., transposition solution to backward stochastic evolution equations

(BSEEs for short). This is something like the generalized function solutions to PDEs. We

obtain the well-posedness of BSEEs in general filtration space, without using the

Martingale Representation Theorem. As an application of our transposition method,

we establish a Pontryagin-type maximum principle for optimal controls of general

infinite dimensional nonlinear stochastic evolution equations, in which both drift and

diffusion terms can contain the control variables, and the control domains are allowed

to be nonconvex.

Global Dynamics of Heterogeneous Lotka-

Volterra Competition-Diffusion Systems

何小清(Xiaoqing He)

华东师范大学

In this talk, we will discuss the joint effects of diffusion and spatial variation on the

global dynamics of a classical Lotka-Volterra competition system. A complete

understanding of the change in dynamics is obtained in terms of diffusion rates and

competition coefficients. To illustrate our understandings, various special cases will be

discussed in the end.

Alberto Bressan, The Pennsylvania State University,USA, [email protected]

Shui-Nee Chow, Georgia Institute of Technology, [email protected]

Yue Liu, University of Texas at Arlington, Texas, USA, [email protected]

John Mallet-Paret, Brown University, USA, [email protected]

Bjorn Sandstede, Brown University, USA, [email protected]

Masaharu Taniguchi( ), Okayama University, Japan, [email protected]

Xiaohui Yu, Shenzhen University, [email protected]

Xinguang Zhang, Curtin University, Australia, [email protected]

, , [email protected]

(Gang Bao), , [email protected]















(Chiun-Chuan Chen), National Taiwan University, [email protected]





(Wenxiong Chen), Yeshiva University, USA, [email protected]


























, Elsevier, [email protected]



, University of Paris-Est, Cr teil, France, [email protected]

















































(Yi Li), Wright State University, USA, [email protected]










(Fanghua Lin), Courant Institute of NYU,USA, [email protected]


















(Yuan Lou), The Ohio State University, USA, [email protected]







(Xinan Ma), , [email protected]






, Univ.of Minnesota, USA, [email protected]




(Xingbin Pan), , [email protected]

(Rui Peng), , [email protected]









(Xiaofeng Ren), The George Washington University, USA, [email protected]













, & , [email protected]















(Xujia Wang), Australian National University, Australia, [email protected]


, The George Washington University, USA, [email protected]























(Xuefeng Wang), Tulane University, USA, [email protected]







(Juncheng Wei), The University of British Columbia, Canada, [email protected]








, McMaster Univ., [email protected]





(Jiangong You), , [email protected]


















(Xu Zhang), , [email protected]



























, Johns Hopkins University, [email protected]


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路线 2:公交 180 路->(莲花南路东川路)->莲花南路校门

路线 3:公交 729 路->(虹梅南路华东师大)->研究生公寓

路线 4:直接乘坐出租车大约需要 80 元(沪闵高架路->S4 沪金高速[收费]剑川路出口下)

人民广场站

(市中心)

路线 1:轨道交通 1 号线->(莘庄站)->见莘庄站

路线 2:轨道交通 8 号线->(江月路站)->闵行 11 路->东川路校门

路线 3:轨道交通 8 号线->(沈杜公路站)->乘坐出租车到达东川路校门大约需要 30 元

路线 4:直接乘坐出租车大约需要 120 元(南北高架->内环高架->沪闵高架->S4 沪金高速[收

费]剑川路出口下)

莘庄站路线 1:轨道交通 5 号线->(东川路站)->闵行 26 路->(东川路莲花南路)->沿东川路步行 700

米->东川路校门

路线 2:轨道交通 5 号线->(东川路站)->乘坐出租车到达东川路校门大约需要 14元

路线 3:公交 816 路->(沪闵路江川路)->公交 958 路->(东川路莲花南路)->莲花南路校门

路线 4:公交 725 路->(莲花南路春申路)->公交 180 路->(莲花南路东川路)->莲花南路校门

路线 5:直接乘坐出租车大约需要 60 元

出租车叫车热线：(+86-21)96822(大众)；(+86-21)6258-0000(强生)

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Documents

第十届华东偏微分方程会议 - East China Normal University · 2015. 6. 9. · Masaharu Taniguchi(谷口雅治) Okayama University, Japan. In this talk I first survey recent