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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五十五)

发布者:戴 情   发布时间:2021-10-08  浏览次数:10

2021非线性分析与偏微分方程学术报告

报告题目1Babuska Problem in Composite Materials and Some Applications

报告人李海刚教授北京师范大学)

会议时间:10月16日(周1000-1100

腾讯会议ID:505 942 292

https: //meeting.tencent.com/dm/Wq9DXYriG45F

 

摘要In high-contrast fiber-reinforced composite materials, the stress concentration between two adjacent inclusions is a common phenomenon, which always causes damage initiation. For the original problem proposed by Ivo Babuska concerning the system of linear elasticity, we develop an iteration technique with respect to the energy integral to overcome the difficulty from the lack of maximal principle in PDE theory and obtain the blow-up asymptotic expressions of the gradients of solutions to the Lame system with partially infinite coefficients in the narrow region between inclusions when they are close to touch. Our results hold for convex inclusions with arbitrary shape and in all dimensions. As an application, we recently proved an extended Flaherty-Keller formula on the effective elastic property of a periodic composite with densely packed fibers, which is related to the “Vigdergauz microstructure” in the shape optimizition of fibers. On the other hand, we recently applied our results to deal with the resonant behavior between two close-to-touching convex acoustic subwavelength resonators.

 

报告人简介李海刚,北京师范大学教授,博士生导师。北京师范大学与美国罗格斯(Rutgers)大学联合培养博士。主要从事材料力学和几何学中偏微分方程理论研究。在复合材料中的Babuska问题、Monge-Ampere方程外Dirichlet问题等方面做出系列结果,在《Adv.Math.》、《Arch. Ration. Mech. Anal.》、《J. Math. Pures Appl.》、《Trans. Amer. Math. Soc.》、《Calc. Var. Partial Differential Equations》、《SIAM J.Math. Anal.》、《J. Differential Equations》等SCI国际权威数学杂志上发表科研论文30余篇。2016年获得教育部霍英东青年教师基金,2018年获得教育部自然科学二等奖(第二获奖人

 

报告题目2Eigenvalue Problems of Hormander Operators on Non-equiregular sub-Riemannian  Manifolds

报告人陈化教授武汉大学)

会议时间:10月16日(周1600-1700

腾讯会议ID:295 326 532

https://meeting.tencent.com/dm/PpDt5OZFknPX

 

摘要We shall report some results on eigenvalue problems for degenerate elliptic operators, which including the results on closed eigenvalue problem and Dirichlet eigenvalue problem of self-adjoint Hörmander operators on non-equiregular sub-Riemannian manifolds. By Rayleigh-Ritz formula and the subelliptic heat kernel estimates ect., we establish the Weyl's asymptotic formula and the precise lower and upper bounds of eigenvalues which depend on the volume of subunit ball and the measure of the manifold. Under a certain condition, we obtain the explicit lower and upper bounds of eigenvalues which have the polynomially growth in k with the optimal order related to the non-isotropic dimension of the manifold.

 

报告人简介陈化, 武汉大学教授,博士生导师,国家杰出青年基金获得者。现为武汉大学数学协同创新中心主任,国务院学科数学评议组成员,湖北省暨武汉数学会理事长,湖北省计算科学省重点实验室主任。主要从事的研究方向为偏微分方程的微局部分析理论,退化型偏微分方程,具生物和医学背景的偏微分方程和偏微分方程的谱理论;主持国家自然科学基金项目18项,其中包括国家杰出青年基金,参加八五、九五、十一五国家重点项目,并主持十二五、十三五国家重点项目以及国家基金委天元基金交叉平台项目等,还为国家重大项目973核心数学项目组成员并获国家教育部跨世纪优秀人才基金。在国际上专业的SCI数学杂志上发表论文100多篇,曾获国家教育部科技进步二等奖两次,2017年主持的科研项目获得国家教育部自然科学奖一等奖。

 

邀请人:非线性分析与PDE团队