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数学学科现代分析及其应用研究所(2021非线性分析与偏微分方程系列报告会五十)

发布者:戴 情   发布时间:2021-07-30  浏览次数:22

报告题目1Concentration on curves for nonlinear Schrödinger problems with electromagnetic potential

报告人赵纯奕 华东师范大学

会议时间:82日(周一),8:30-9:30

腾讯会议ID:  659 916 135

https://meeting.tencent.com/s/je8wGdNIqO6B

 

摘要我们将研究带磁薛定谔方程的解的曲线型集中现象, 讨论集中现象所在的曲线与电磁场之间的联系.

报告人简介赵纯奕,华师范大学副教授。主要从事偏微分方程的研究, 主要成果发表在《JDE》、《Calc.Var. PDE》、《Arch. Rat. Mech. Anal,SIAM J. Math. Anal》、《C. R. Math. Acad. Sci. Paris》、《Proc. Roy. Soc. Edinburgh Sect. A》、Discrete Contin. Dyn. Syst.等国际学术期刊

报告题目2 Homogenization of Singular Perturbed Elliptic Systems

报告人纽维生(安徽大学)

会议时间:82日(周一),9:30-10:30

腾讯会议ID:  659 916 135

https://meeting.tencent.com/s/je8wGdNIqO6B

 

摘要We discuss quantitative estimates in periodic homogenization of second-order elliptic systems of elasticity with singular fourth-order perturbations. The convergence rates, which depend on the scale $\kappa$ that represents the strength of the singular perturbation and on the length scale $\varepsilon$ of the heterogeneities, will be presented. We also give the large-scale Lipschitz estimate, down to the scale $\varepsilon$ and independent of $\kappa$. This is a joint work with Pro. Zhongwei Shen.

报告人简介纽维生,安徽大学副教授,2011年毕业于兰州大学。目前主要研究兴趣为偏微分方程及动力系统的齐次化问题,在高阶椭圆、抛物方程的齐次化问题的研究上取得了非常优秀的的成果。在Journal of Functional Analysis,Discrete and Continuous Dynamical Systems等期刊上发表多篇论文。

 

报告题目3: Existence of Sign-changing self-similar solutions for the H\'enon type parabolic equation  

报告人王俊(江苏大学)

会议时间:82日(周一),14:30-15:30

腾讯会议ID:  353 761 064

https://meeting.tencent.com/s/ByXFhjIG2hfA

 

摘要In this talk, we introduce the existence self-similar solutions for the H\'enon parabolic equation $\phi_t-\Delta \phi=|x|^\beta |\phi|^{\alpha-1}\phi$ with the initial data $\phi_0(x)$. First, we prove the existence for non-unique solution in $\mathbb{R}^N(N\geq1)$ by examining self-similar solution of the H\'enon parabolic equation. Second, we show the existence of positive regular solutions of the Cauchy problem for the equation with $\phi_0(x)=\eta\phi_*$ for all $\eta>1$ close enough to $1$ in $\mathbb{R}^N(N\geq3)$, where $\phi_*$ is the singular stationary solution in $\mathbb{R}^N$. Third, we prove the existence of infinitely many sign-changing self-similar solutions to the Cauchy problem with positive initial value. Finally, we derive Liouville type results and existence of periodic solutions for the parabolic system with nonhomogeneous nonlinearities.   

报告人简介王俊,教授,博士生导师,江苏大学数学科学学院副院长。东南大学应用数学博士毕业,台湾大学博士后。2018年破格晋升为教授。2020年获江苏省杰青,“全国百篇优秀博士论文提名论文”,首届江苏省优青、江苏省“333高层次人才培养工程”中青年学科带头人和“六大人才高峰”高层次人才项目,2019年获教育部自然科学二等奖(排名第二),并被遴选为江苏大学“优秀青年学术带头人”。主要从事非线性泛函分析及其应用研究,在CPDE,CVPDE, Nonlinearity, Annales Henri Poincare和JDE等权威期刊发表多篇学术论文。主持国家面上项目2项,主持国家青年基金及其他省部级项目6项。先后应邀访问美国威廉玛丽学院和香港理工大学等高校。

报告人题目4Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate

报告人崔仁浩(哈尔滨师范大学)

会议时间:82日(周一),15:30-16:30

腾讯会议ID:  353 761 064

https://meeting.tencent.com/s/ByXFhjIG2hfA

 

摘要We are concerned with a reaction-diffusion SIS epidemic model with saturated incidence rate in advective heterogeneous environments. The existence of the endemic equilibrium (EE) is established when the basic reproduction number is greater than one. We further investigate the effects of diffusion, advection and saturation on asymptotic profiles of the endemic equilibrium. The individuals concentrate at the downstream end when the advection rate tends to infinity. As the diffusion rate of the susceptible individuals tends to zero, a certain portion of the susceptible population concentrates at the downstream end, and the remaining portion of the susceptible population distributes in the habitat in a non-homogeneous way; on the other hand, the density of infected population is positive on the entire habitat. The density of the infected vanishes on the habitat for small diffusion rate of infected individuals or the large saturation. The results may provide some implications on disease control and prediction.

报告人简介崔仁浩,哈尔滨师范大学数学科学学院教授,硕士生导师。主要从事非线性分析、偏微分方程及其应用方向的研究,在空间异性中反应扩散系统的动力学行为方面的研究取得了一定的进展,在国际著名学术期刊J. Differential Equations 等学术刊物上发表论文多篇;主持完成国家自然科学基金青年项目、全国博士后基金及黑龙江省自然科学基金等项目;作为主要完成人获得黑龙江省科学技术(自然科学)二等奖一项。2018年获黑龙江省数学会第二届优秀青年学术奖。

邀请人:非线性分析与PDE团队