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【6月17日】非线性分析和偏微分方程研讨会

发布时间:2023-06-05文章来源:002cc白菜资讯蒋继强 浏览次数:

报告一

窦井波教授学术报告

报告题目Reversed Hardy-Littlewood-Sobolev inequalities with vertical weights on the upper half space

:窦井波 教授 陕西师范大学

   2023年6月17日上午(星期六) 8:30-9:30

   :002cc白菜资讯304室学术报告厅

   In this talk, we establish the reversed Hardy-Littlewood-Sobolev inequality with vertical weights on the upper half space and discuss the extremal functions. We show that the sharp constants in this inequality are attained by introducing a renormalization method. The classification of corresponding extremal functions is discussed via the method of moving spheres. Moreover, we prove the sufficient and necessary conditions of existence for positive solutions to the Euler-Lagrange equations by using Pohozaev identities in weak sense. This is joint work with Yunyun Hu and Jingjing Ma.

报告人简介:窦井波,教授,博士生导师。现为陕西师范大学数学与统计学院教授。研究方向是偏微分方程理论及其应用。近年来与多位合作者集中研究最优几何不等式及其椭圆方程解的存在性等问题。在Adv. Math.,J. Funct. Anal.,Inter. Math. Res. Notices, J. Diff. Equ.等国际学术期刊上发表学术论文40余篇;主持国家自然科学基金3项,2019 年获陕西省杰出青年科学基金项目,2022年获陕西高校青年创新团队项目。

 

报告二

张彬林教授学术报告

报告题目Some progress on singular Kirchhoff-type problems

:张彬林 教授 山东科技大学

   2023年6月17日上午(星期六) 9:30-10:30

   :002cc白菜资讯304室专家报告厅

   In this talk, we discuss some Kirchhoff-type singular problems involving subcritical and critical nonlinearities. By combining variational methods with some delicate techniques, we obtain the existence, uniqueness and multiplicity of solutions for above problems. Here we point out that our methods could be applied to more elliptic equations with subcritical and critical growth. This is joint works with L. Wang, C. Lei and V. Radulescu.

报告人简介:张彬林,山东科技大学教授,博士生导师。博士毕业于哈尔滨工业大学,先后在意大利地中海研究中心和南开大学陈省身数学研究所做过两站博士后。当前的研究兴趣是变分和拓扑方法及其在数学物理问题中的应用,特别在非局部偏微分方程解的存在性、多解性等方面取得了一系列研究结果。在CVPDE, JDE, Nonlinearity, JGA, DCDS等知名期刊上发表SCI论文100余篇,担任多个SCI期刊编委。主持和参与多个国家自然科学基金项目。2019年和2021年分别入选科睿唯安“全球高被引科学家”名单,2022年入选爱思唯尔“中国高被引学者”名单。

 

报告三

蒋永生教授学术报告

报告题目On the Schrödinger-Poisson equations with external potential

:蒋永生 教授 中南财经政法大学

   2023年6月17日上午(星期六) 10:50-11:50

   :002cc白菜资讯304室专家报告厅

   In this talk, we consider a class of Schrödinger-Poisson equations with external potential. Precisely, via a variational analysis and a priori estimates for nonlinear elliptic equations, we give sufficient conditions for the existence, nonexistence and multiplicity of solutions to the Schrödinger-Poisson equations with various external potentials. 

报告人简介蒋永生,中南财经政法大学教授,博士生导师。主要研究方向为偏微分方程,非线性泛函分析及其应用等。研究结果发表在Math. Ann., J. Funct. Anal., Calc. Var. PDE, J. Differential Equations, Sci. China Math.等学术期刊上。


报告四

代国伟教授学术报告

报告题目Two new global bifurcation theorems and their applications

:代国伟 教授 大连理工大学

   2023年6月17日下午(星期六) 14:30-15:30

   :002cc白菜资讯304室学术报告厅

   In this topic, we introduce two new global bifurcation theorems: the unilateral global bifurcation theorem about Fredholm operator with index 1 and the analytic global bifurcation theorem. As their applications, we obtain the bifurcation structure for an overdetermined problem and the bifurcation structure for a nonlinear pseudodifferential equation, which describes the periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. In particular, we show the existence of Stokes' highest wave.

报告人简介:代国伟,大连理工大学教授,博士生导师。研究方向是分歧理论及应用。在《Indiana Univ. Math. J.》、《J. Funct. Anal.》、《Calc. Var. Partial Differential Equations》、《J. Differential Equations》、《Nonlinearity》等上发表学术论文100余篇。所发论文被引用913次。在科学出版社出版学术专著1部。主持完成国家自然科学基金2项,正在主持面上基金1项。2020年和2021年连续两次入围国家优青答辩。2022年入选“天元东北中心优秀青年学者奖励计划”。2018年入选辽宁省“百千万人才工程”万层次人选。2019年入选大连市高端人才支持计划。2017 年入选大连理工大学“星海学者”人才培养计划中的“星海优青”工程。获高校科技进步奖一等奖3次,省自然科学奖二等奖1次。

 

报告五

陈鹏玉教授学术报告

报告题目Existence and stability of random attractors for 3D BBM equations driven by nonlinear noise

:陈鹏玉 教授 西北师范大学

   2023年6月17日下午(星期六) 15:30-16:30

   :002cc白菜资讯304室学术报告厅

   In this talk I will introduce our recent work on the long time behavior of the solutions of the non-autonomous Benjamin-Bona-Mahony equation driven by nonlinear colored noise with continuous coefficients defined on three-dimensional unbounded channels. The solutions of the equation are not unique and hence generate a multivaluednon-autonomous random dynamical system. We first prove the measurability of the multivalued random system bythe idea of weak upper semicontinuity of solutions, and then establish the existence and uniqueness of tempered pullback random attractors based on the pullback asymptotic compactness of solutions. The difficulty of the non-compactness of Sobolev embeddings on unbounded domains is overcome by the methods of the spectral decomposition inside bounded domains as well as the uniform tail-estimates of solutions outside bounded domains. Furthermore, the backward compactness and asymptotically autonomous robustness of pullback random attractors of non-autonomous Benjamin-Bona-Mahony equations driven by nonlinear colored noise defined on 3D unbounded channels has also been established.

报告人简介:陈鹏玉, 理学博士,西北师范大学数学与统计学院教授,兼任美国《Math Review》和德国《Zentralblatt MATH》评论员。 2022年入选甘肃省“飞天学者”特聘计划,2021年获甘肃省杰出青年基金资助。主要从事非线性分析与随机动力系统的研究,在国际著名数学刊物Mathematische Annalen、Journal of Geometric Analysis等上发表学术论文50余篇。主持国家自然科学基金2项,甘肃省杰出青年基金和甘肃省自然科学基金重点项目各1项。研究成果获甘肃省自然科学奖二等奖和三等奖各1项。

 

报告六

李锦路教授学术报告

报告题目Fan-KKM Theorem and Schauder's conjecture

:李锦路 教授 Shawncee State University (美国)

   2023年6月17日下午(星期六) 16:50-17:50

   :002cc白菜资讯304室学术报告厅

   Schauder's conjecture (Problem 54 in The Scottish Book) was raised out about one hundred years ago. We apply the Fan-KKM theorem to prove some fixed point theorems, which are partially solved the Schauder's fixed point problem. We also apply the Fan-KKM theorem to prove some fixed point theorems in metric vector spaces, in which the considered mappings are not required to be continuous.

报告人简介李锦路博士、教授,早期毕业于北京大学。而后获得美国Wayne State University博士学位。在美国Wayne State University和Shawnee State University数学系从教三十多年,一直从事函数论、算子理论及不动点理论和应用的研究。近年来,致力于赋序集上的不动点理论和应用的研究,首次证明了链完备半序集上的集值映射不动点定理,并在赋序变分方程、具有半序效益函数的博弈中广义 Nash均衡点的存在性,以及一些积分方程的可解性等领域得到许多应用,解决了拓扑半序空间中存在交替的闭拓扑算子和可传递算子不稳定的长期未解决的问题,在国际专业期刊上发表论文 110余篇。

 

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