报告题目1：Propagation dynamics of the monostable reaction-diffusion equation with a new free boundary condition

报告人：杜一宏，澳大利亚新英格兰大学

报告时间：2024年4月26日上午

报告地点：20-404

报告摘要：I will report some recent results on the reaction diffusion equation  $u_t-du_{xx}=f(u)$ with a monostable nonlinear function $f(u)$ over a changing interval $[g(t), h(t)]$, viewed as a model for the spreading of a species with population range $[g (t), h(t)]$ and density $u(t,x)$. The free boundaries $x=g(t)$ and $x=h(t)$ are not governed by the same Stefan condition as in Du and Lin (2010) and other previous works; instead, they satisfy a related but different set of equations obtained from a “preferred population density” assumption at the range boundary, which allows the population range to shrink as well as to expand. I will demonstrate that the longtime dynamics of the model exhibits persistent propagation with a finite asymptotic propagation speed determined by a certain semi-wave solution, and the density function converges to the semi-wave profile as time goes to infinity. The asymptotic propagation speed is always smaller than that of the corresponding classical Cauchy problem where the reaction-diffusion equation is satisfied for $x$ over the entire real line with no free boundary. Moreover, when the preferred population density used in the free boundary condition converges to 0, the solution $u$ of our free boundary problem converges to the solution of the corresponding classical Cauchy problem, and the propagation speed also converges to that of the Cauchy problem.

报告人简介： 杜一宏，博士生导师，1962年出生。于1978年至1988年在山东大学获得学士、硕士和博士学位，导师为郭大钧教授。1988年至1991年赴英国Heriot-Watt University大学做Research Fellow，1991年至1992年在澳大利亚新英格兰大学做Research Fellow，合作导师为国际著名数学家E.N. Dancer教授。随后历任澳大利亚新英格兰大学讲师、高级讲师、副教授、教授。目前主要研究兴趣包括非线性椭圆型和抛物型偏微分方程、自由边界问题、非线性泛函分析及其应用。已在国际一流数学杂志包括JEMS、ARMA、PLMS、JFA、JMPA、TAMS、AIHP、SIAM、IUMJ、CVPDE、Nonlinearity、JDE等发表学术论文170余篇。已发表论文完全他引次数超过5000次，多次入选Web of Science高被引学者。出版个人研究专著1部。多次组织国际性学术会议，多次担任国际大会执行和学术委员会委员，多次被邀请参加国际学术会议并做全会报告或者邀请报告。获校长杰出研究奖(Vice-Chancellor's Award for Excellence in Research)。已连续多次主持澳大利亚国家研究基金（ARC）。

报告题目2：Pattern dynamics in a vegetation-water model with human activities: an optimal control approach

报告人：孙桂全，中北大学

报告时间：2024年4月26日上午

报告地点：20-404

报告摘要：Desertification in arid regions is usually accompanied by a shift in vegetation patterns. Much effort has been devoted to investigating shifts in vegetation patterns caused by changes in key parameters or parameter space. But little has been done in terms of how to achieve shifts with constant parameter space. To this end, we study the shift in plant patterns caused by human activity using a conventional dryland vegetation-water model integrated with optimal control theory. We found that human action can produce many forms of pattern shifts, such as shifts between stationary patterns, non-stationary patterns, as well as stationary and non-stationary patterns, while maintaining the parameter space constant and the cost low.

报告人简介：孙桂全，中北大学教授，数学学院院长，博士生导师，中国数学会生物数学专委会副主任，中国青年科技工作者协会理事。主要从事斑图动力学和传染病传播动力学研究，在Physics Reports、Physics of Life Reviews、J. Differential Equations、SIAM J. Appl. Math.、Nonlinearity等国内外期刊发表论文60余篇。主持国家重点研发计划1项，国家自然科学基金项目4项，获得霍英东教育基金会青年教师基金、“博士后国际交流计划”、“山西省优秀科技工作者”和“山西省青年五四奖章”。以第一完成人获得山西省科技奖一等奖1项。

报告题目3：Some delay-induced nonlocal problems

报告人：方健，哈尔滨工业大学

报告时间：2024年4月26日上午

报告地点：20-404

报告摘要：In this talk, I will first recall some classical nonlocal population models induced by time delay, and then I will present a few new models by considering joint effects of time delay and other factors.

报告人简介：方健，哈尔滨工业大学数学学院教授、副院长。2005年于大连理工大学获学士学位后，到哈尔滨工业大学攻读基础数学博士学位，2011年留校任讲师，2012年晋升为教授。2007至2010年，作为联合培养博士生在加拿大纽芬兰纪念大学学习，2011至2015年分别在加拿大约克大学和法国社会科学高等研究院做博士后研究。曾获全国优博提名和首届秦元勋青年数学奖。目前主要从事扩散系统的时空传播理论及应用研究，在JEMS、JMPA、MathAnn等期刊发表论文二十余篇，主持和参加多项国家自然科学基金项目。

报告题目4：Blow up analysis for a parabolic MEMS problem

报告人：王克磊，武汉大学

报告时间：2024年4月26日上午

报告地点：20-404

报告摘要：Microelectromechanical system (MEMS) is a widely used device in industry and technology. The mathematical modeling of this system involves a class of PDEs with singular nonlinearity of the form u^{-p}, where the zero set of the solution,{u=0}, describes the rupture phenomena in MEMS. The rigorous mathematical analysis of this rupture phenomena has been studied by many people for a long time. But generally the asymptotic behavior of solutions near the rupture set is still not well understood. In this talk I will discuss a blow up analysis approach to this problem.

报告人简介：王克磊，现为武汉大学数学与统计学院教授。他2010年于中科院数学所获博士学位，曾在悉尼大学从事博士后研究及（原）中科院武汉物理与数学研究所工作。他的研究兴趣主要在于椭圆与抛物型偏微分方程的几何与定性性质方面，尤其是与几何测度论问题相关的奇性分析问题，例如相位分离模型及其极限自由边界问题、非线性椭圆方程的稳定解与有限Morse指标解、Allen-Cahn方程的De Giorgi猜想及有限Morse指标解的分类问题等。

报告题目5：A three-dimensional Keller-Segel-Navier-Stokes system involving subquadratic logistic degradation

报告人：向昭银，电子科技大学

报告时间：2024年4月26日上午

报告地点：20-404

报告摘要：In this talk, we consider a Keller-Segel-Navier-Stokes system involving subquadratic logistic degradation in a three-dimensional smoothly bounded domain along with reasonably mild initial conditions and no- flux/no-flux/Dirichlet boundary conditions for cell population/ chemical/fluid. The purpose of the present talk is to firstly show the generalized solvability for the model under some subquadratic logistic exponent restriction, which indicates that persistent Dirac-type singularities can be ruled out, and to secondly exhibit the eventual smoothness of these solutions under the stronger restriction whenever linear growth coefficient of population is not too large. These results especially extend the precedent works due to Winkler (J. Funct. Anal. 276 (2019): 1339-1401; Comm. Math. Phys. 367 (2022): 439-489.), where, among other things, the corresponding studies focus on the case of quadratic degradation.

报告人简介：向昭银，电子科技大学数学科学学院教授、博士生导师。2006年博士研究生毕业于四川大学。目前主要从事偏微分方程的研究，在CPDE、CVPDE、IMRN、JFA、Math Z 等期刊上发表学术论文 70 余篇，作为负责人主持多项国家自然科学基金项目。

报告题目6：格点扩散系统的主特征值与行波解

报告人：梁兴，中国科学技术大学

报告时间：2024年4月26日下午

报告地点：20-404

报告摘要：这个报告将介绍一维格点薛定谔算子和雅可比算子的主特征值问题的一些进展及其在行波解、解的均质化理论等问题中应用。

报告人简介：梁兴，中国科学技术大学教授，博士生导师，获得全国百篇优秀博士论文、中国数学会钟家庆数学奖等多项称号。主持多项国家自然科学基金项目。主要研究兴趣为抛物系统和扩散系统的时空动力学及相关问题，已在CPAM、JMPA、PLMS 、Adv. Math、Math Ann、TAMS、JFA、JDE等数学杂志发表学术论文多篇。工作被动力系统、偏微分方程、生物数学界同行广泛引用。

报告题目7：Threshold dynamics of a nonlocal and delayed cholera model in a spatially heterogeneous environment

报告人：汪翔升，美国路易斯安那大学拉菲特分校

报告时间：2024年4月26日下午

报告地点：20-404

报告摘要：A nonlocal and delayed cholera model with two transmission mechanisms in a spatially heterogeneous environment is derived. We introduce two basic reproduction numbers, one is for the bacterium in the environment and the other is for the cholera disease in the host population. If the basic reproduction number for the cholera bacterium in the environment is strictly less than one and the basic reproduction number of infection is no more than one, we prove globally asymptotically stability of the infection-free steady state. Otherwise, the infection will persist and there exists at least one endemic steady state. For the special homogeneous case, the endemic steady state is actually unique and globally asymptotically stable. Under some conditions, the basic reproduction number of infection is strictly decreasing with respect to the diffusion coefficients of cholera bacteria and infectious hosts. When these conditions are violated, numerical simulation suggests that spatial diffusion may not only spread the infection from high-risk region to low-risk region, but also increase the infection level in high-risk region.

报告人简介：汪翔升，2009年获得香港城市大学博士学位；2009-2013年先后在香港城市大学，加拿大York大学、Memorial University of Newfoundland大学从事博士后研究工作；现在任职于美国University of Louisiana at Lafayette大学，主要研究渐近分析、微分动力系统、生物数学和计算数学。迄今为止已在Advances in Mathematics、J. Math. Pures Appl.、SIAM J. Control and Optimization、Studies in Applied Mathematics、JDE、JDDE、BMB、JTB等期刊上发表学术论文60余篇。

报告题目8：Dynamics of Lotka-Volterra competition patch models

报告人：陈珊珊，哈尔滨工业大学威海分校

报告时间：2024年4月26日下午

报告地点：20-404

报告摘要：In this talk, we mainly consider two-species competition models in advective patchy environments. The models can also be viewed as discrete versions for the corresponding reaction-diffusion-advection models. For spatially heterogeneous case, we investigate three types of three-patch river network modules and show that river networks affect the global dynamics of the models. For varying drift case, we show that the convexity of the drift rates has a significant impact on the competition outcomes: if the drift rates are convex, then the species with the larger diffusion rate wins the competition; if the drift rates are concave, then the species with the smaller diffusion rate wins the competition.

报告人简介：陈珊珊，哈尔滨工业大学（威海）数学系教授，博士生导师，主要研究方向是微分方程的分支理论及其在生物数学上的应用，已在CVPDE，SIAP，JDE等SCI杂志发表论文30余篇，目前主持国家自然科学基金面上项目1项。

报告题目9：Critical exponent in a fully parabolic Keller-Segel system with prescribed signal on the boundary

报告人：王玉兰，西华大学

报告时间：2024年4月26日下午

报告地点：20-404

报告摘要：In this talk, we will discuss a fully parabolic Keller-Segel system in a bounded domain with smooth boundary. In contrast to most literature addressing the no-flux/no-flux boundary value problem for chemotaxis systems, we require inhomogeneous Dirichlet signal boundary condition here. A critical exponent distinguishing the global solvability and finite-time singularity is obtained.

报告人简介：王玉兰，博士，教授，主要从事非线性偏微分方程的研究，近几年的研究兴趣主要为趋化方程组的性质，已在“Comm.Partial Differential Equations”、“Calc.Var. Partial Differential Equations”、“Math Z”、“Math. Models Methods Appl. Sci.”、“ASNS. Pisa”、“J. Differential Equations”、“Proc. Roy. Soc. Edinburgh Sect. A”、“Commun. Math. Sci.”、“Discrete Contin. Dyn. Syst.”等国际数学期刊上发表学术论文近30篇；先后主持国家自然科学基金项目、四川省应用基础研究项目、中央引导地方科技发展专项项目等；获得四川省科技进步奖（自然科学类）二等奖。

报告题目10：Nonlinear stability of shock profiles to Burgers equation with critical fast diffusion and singularity

报告人：李敬宇，东北师范大学

报告时间：2024年4月26日下午

报告地点：20-404

报告摘要：In this talk we propose the first framework to study Burgers' equation featuring critical fast diffusion in form of $u_t+f(u)_x = (\ln u)_{xx}$. The solution possesses a strong singularity when $u=0$ hence bringing technical challenges. Our main purpose is to investigate the asymptotic stability of viscous shocks, particularly those with shock profiles vanishing at the far field $x=+\infty$. To overcome the singularity, we introduce some weight functions and show the nonlinear stability of shock profiles through the weighted energy method.

报告人简介：李敬宇，东北师范大学教授，主要关注生物趋化方程及流体力学方程的数学理论研究。在Proc. London Math. Soc., SIAM J. Math. Anal., Math. Models Methods Appl. Sci., J. Differential Equations等期刊发表多篇论文。

邀请人：非线性分析与PDE团队