《2017年人民大学冬季PDE研讨会》
为交流近年来在偏微分方程及其应用领域所取得的最新研究成果，研讨相关的前沿课题，同时促进偏微分方程相关领域的青年学者间的合作研究，中国人民大学数学科学研究院定于2017年11月25日至26日举行《2017年人民大学冬季PDE研讨会》。本次会议共有13个邀请报告，我们诚邀各位老师、专家学者、研究生、博士后等参加。
本次会议不收取会务费，交通费、食宿费用等均需自理。
会议组织者：向田 （13718906155， txiang@ruc.edu.cn）
会务组：
方亦豪 耿云凤 姜红岩
王钧 （01062519572, wangjunruc@ruc.edu.cn）
向田 闫丽丽 张聪晖
会议时间：2017年11月25日，8:0018: 00
2017年11月26 早上自由讨论，下午离会。
地点：中国人民大学国学馆110教室
承办单位：中国人民大学数学科学研究院
中国人民大学数学科学研究院
2017年11月24日
2017人民大学冬季PDE研讨会
2017 Winter Symposium for PDE
Renmin University
会议程序册
Program and Abstract
November 2526, 2017
Renmin University of China, Beijing, China
Hosts: Institute for Mathematical Sciences
Renmin University of China
Supported by: Renmin University of China,
National Nature Science Foundation of China
2017人民大学冬季PDE研讨会
2017年11月2526日
中国人民大学国学馆110教室
演讲嘉宾：
边东芬 
北京理工大学 
金春花 
华南师范大学 
金海洋 
华南理工大学 
李 静 
中央民族大学 
李 青 
首都师范大学 
林 可 
西南财经大学 
刘 爽 
中国人民大学 
彭英萍 
电子科技大学 
孙宁奎 
山东师范大学 
王一夫 
北京理工大学 
谢 莉 
西华师范大学 
赵相东 
大连理工大学 
郑 攀 
重庆邮电大学 
组织委员会：
向 田 (13718906155, txiangg@ruc.edu.cn）中国人民大学
会务组：
方亦豪
耿云凤
姜红岩
刘 爽 （liushuangnqkg@ruc.edu.cn）
王 钧 （01062519572, wangjunruc@ruc.edu.cn）
向 田
闫丽丽
张聪晖
Schedule


Saturday morning ( November 25th) 

Venue: 110, Guoxueguan Building (国学馆110教室), Renmin University of China (中国人民大学国学馆110教室, 图书馆西侧) 

7:508:20 
Registration ( 110, Guoxueguan Building ) 
8:208:30 
Opening ceremony 
Session I 
Chair: 郑斯宁 
8:309:05 
王一夫, 北京理工大学, Global boundedness of solutions to a chemotaxis—haptotaxis model with tissue remodeling 
9:059:35 
郑攀, 重庆邮电大学 Persistence and boundedness of solutions for twospeices chemotaxis model with two signals 
9:3510:05 
边东芬, 北京理工大学 Global wellposedness of nonisothermal inhomogeneous nematic liquid crystal flow 
10:0510:25 
Group Photo and Tea Break 
Session II 
Chair: 柯媛元 
10:2511:00 
金春花, 华南师范大学 Global Solvability and Boundedness to a Coupled ChemotaxisFluid Model with Arbitrary Porous Medium Diffusion 
11:0011:30 
李静,中央民族大学 Large time behavior of solutions to a fully parabolic attractionrepulsion chemotaxis system with logistic source 
11:3012:00 
赵相东, 大连理工大学 Asymptotic behavior to a chemotaxis consumption system with singular sensitivity 
12:0014:00 
Lunch Break (Huixian Restaurant 汇贤府) 
Saturday afternoon (November 25th) 

Session III 
Chair: 吴雅萍 
14:0014:35 
谢莉, 西华师范大学 On a twospecies chemotaxis system with two chemicals and competitive kinetics 
14:3515:05 
孙宁奎, 山东师范大学 FisherKPP equation with free boundaries and timeperiodic advections 
15:0515:35 
彭英萍, 电子科技大学 Global Solutions to the Coupled ChemotaxisFluids System in a 3D Unbounded Domain with Finite Depth 
15:3515:50 
Tea Break 
Session IV 
Chair: 向田 
15:5016:25 
金海洋, 华南理工大学 Global stabilization of the full attractionrepulsion chemotaxis model 
16:2516:55 
林可,西南财经大学
Large time behavior in a higherdimensional attractionrepulsion chemotaxis system

16:5517:25 
李青,首都师范大学
Stability of steady states for SKT competition system with crossdiffusion

17:2517:55 
刘爽, 中国人民大学 Monotonicity of principal eigenvalue for elliptic operators with incompressible flow

18:0020:00 
Dinner (Huixian Restaurant) 
Sunday morning ( November 26th) 

自由讨论 
Title and Abstract
Global wellposedness of nonisothermal inhomogeneous nematic liquid crystal flow
边东芬
北京理工大学
Email address: biandongfen@bit.edu.cn
Abstract: This paper is devoted to studying the temperaturedependent incompressible nematic liquid crystal flows in a bounded domain . The global wellposedness for small perturbation around the trivial equilibrium state is established. This is a joint work with Dr. Yao Xiao.
Global Solvability and Boundedness to a Coupled ChemotaxisFluid Model with Arbitrary Porous Medium Diffusion
金春花
华南师范大学
Email address: jinchhua@126.com
Abstract: We consider a coupled chemotaxisfluid model with zeroflux boundary and noslip boundary. It is shown that for any large initial datum, for any $m>0$, $\alpha>0$, the problem admits a global weak solution, which is uniformly bounded. On the basis of this, the stability of the steady states also be discussed.
Global stabilization of the full attractionrepulsion chemotaxis model
金海洋
华南理工大学
Email address: mahyjin@scut.edu.cn
Abstract: In this talk, we are concerned with the full attractionrepulsion chemotaxis system with different diffusion coefficients of the two chemical signal. By constructing some appropriate Lyapunov functions, we establish the boundedness and asymptotical behaviors of solutions to the system with large initial data in a twodimensional bounded domain under the homogeneous Neumann boundary conditions. This is a joint work with Prof. Zhian Wang.
Large time behavior of solutions to a fully parabolic attractionrepulsion chemotaxis system with logistic source
Abstract: The purpose of this talk is to mathematically understand the effect of the attractive signal, the repulsive one and the logistic source on the global boundedness and asymptotic behavior of solutions to a fully parabolic attractionrepulsion chemotaxis system with logistic source in the higherdimensional setting.
Stability of steady states for SKT competition system with crossdiffusion
首都师范大学
Email address: qingli_324@163.com
Abstract: In this talk, we shall concerned with a quasilinear reaction diffusion system with cross diffusion, which was first proposed by Shigeseda, Kawasaki and Teramoto in 1979 for investigating the spatial segregation of two competing species under inter and intraspecies population pressures. I will talk about some resent research progress on the existence and stability of some types of nontrivial steady states for the SKT competition model as one of the cross diffusion rate is large enough, which may correspond to some new pattern formation induced by cross diffusion. This is a joint work with Professor Yaping Wu.
Large time behavior in a higherdimensional attractionrepulsion chemotaxis system
Email address: linke@swufe.edu.cn
Abstract: In this talk we consider the long time behavior of solutions to an attractionrepulsion chemotaxis system in a bounded domain under zeroflux boundary conditions if repulsion dominates over attraction. It is known that under the assumption that repulsion balances/cancels attraction, for any suitably regular initial data all solutions of this problem will be global and bounded. We further show that if the degradation rate of a repulsive signal is smaller than the attractive one or the repulsion is suitable strong, these global solutions converge to the steady state for arbitrarily large initial data.
Monotonicity of principal eigenvalue for elliptic operators with incompressible flow
Email address: liushuangnqkg@ruc.edu.cn
Abstract: In this talk, we establish the monotonicity of the principal eigenvalue , as a function of the advection amplitude , for the elliptic operator with incompressible flow , subject to Dirichlet, Robin and Neumann boundary conditions. As a consequence, the limit of as always exists and is finite for Robin boundary conditions. These results answer some open questions raised by Berestycki, Hamel and Nadirashvili (CMP 2005). This is a joint work with Prof. Yuan Lou.
Global Solutions to the Coupled ChemotaxisFluids System in a 3D Unbounded Domain with Finite Depth
Email address: yingping_peng@163.com
Abstract: we will investigate the global existence of solutions to a coupled chemotaxisfluids system in a three dimensional unbounded domain with finite depth. In the chemotaxisNavierStokes case, we establish the global existence and uniqueness of strong solutions around a constant state, while in the chemotaxisStokes case, we show the global existence of weak solutions for large initial cell density and velocity. Our proof is based on some uniform a priori estimates obtained by using the anisotropic Lp technique and the elliptic estimates. To the best of our knowledge, this is the first analytical work for the wellposedness of chemotaxisfluids system in an unbounded domain with boundary. Our results are consistent with the experiment observation and numerical simulation.
FisherKPP equation with free boundaries and timeperiodic advections
Email address: sunnk1987@163.com
Abstract: We consider the FisherKPP equation with free boundaries and timeperiodic advections. We are interested in the long time behavior of solutions. When the advection is small, we give a vanishingspreading dichotomy results; when the advection is mediumsized, we show a vanishingtransitionvirtual spreading trichotomy result; when the advection is large, we prove that vanishing happens for all solutions. Moreover, we give the estimate for the spreading speed of the spreading/virtual spreading solutions. There is a joint work with Bendong Lou and Maolin Zhou.
Global boundedness of solutions to a chemotaxis—haptotaxis model with tissue remodeling
Abstract: This talk is concerned with a cancer invasion model comprising a strongly coupled PDEODE system in two and three space dimensions. The system consists of a parabolic equation describing cancer cell migration arising from a combination of chemotaxis and haptotaxis, a parabolic/elliptic equation describing the dynamics of matrix degrading enzymes (MDE), and an ODE describing the evolution and remodeling of the extracellular matrix (ECM). We point out that this strongly coupled PDEODE setup presents new mathematical difficulties, which are overcome by developing new integral estimate techniques.We prove that the system admits a unique global classical solution which is uniformly bounded in time in the twodimensional spatial setting at all cancer cell proliferation rates. We also prove that, in the case of threedimensional convex spatial domain, when cancer cell proliferation is suitably small, the system also possesses a unique classical solution for appropriately small initial data. These results improve previously known ones.
On a twospecies chemotaxis system with two chemicals and competitive kinetics
Abstract: This work is devoted to the twospecies chemotaxis system with two chemicals and LotkaVolterra competitive kinetics. There are few results on chemotaxis system with two different chemicals. Recently, in the absence of population competition, the global existence of the above system were established in the 2dimensional case for parabolicelliptic case (Tao & Winkler, 2015,DCDSB) and parabolicparabolic case (Li & Wang, 2016, DCDSB) respectively. The purpose of this work is firstly to give global existence and boundedness of solutions to the fully parabolic system with LotkaVolterra competitive kinetics, and then, under some conditions on the parameters, to establish the large time behavior of solutions.
Asymptotic behavior to a chemotaxis consumption system with singular sensitivity
赵相东
大连理工大学
Email address: Zhaoxd_521@163.com
Abstract: We consider a chemotaxis consumption system with singular sensitivity $u_t=\Delta u\chi\nabla\cdot(\frac{u}{v^\alpha}\nabla v)$, $v_t=\epsilon\Deltavuv$ in a bounded domain $\Omega\subset\mathbb{R}^n$ with $\chi,\alpha,\epsilon>0$. It is proved that there exists a global classical solution with $n=1$. In particular, for any global classical solution $(u,v)$ to the case of $\alpha\ge 1$, it is shown that $v$ converses to $0$ in the $L^\infty$norm as $t\rightarrow\infty$ with the decay rate established whenever $\epsilon\in(0,1)$ appropriately large, rather than those in the $L^p$sense as generally obtained.
Persistence and boundedness of solutions for twospeices chemotaxis model with two signals
Email address: zhengpan@cqupt.edu.cn
Abstract: In this talk, we consider a twocompetingspecies chemotaxis system with two different chemicals under homogeneous Neumann boundary conditions in a smooth bounded domain. Firstly, when , based on some a priori estimates and MoserAlikakos iteration, it is shown that regardless of the size of initial data, for any positive parameters, the system possesses a unique globally bounded classical solution if $n=2$. On the other hand, when , relying on the maximal Sobolev regularity and semigroup technique, it is proved that the system admits a unique globally bounded classical solution provided that $\mu_{1}$ and $\mu_{2}$ are suitably large. Finally, under the noncompetition case, we study the persistence property of mass for this model.