报告题目1：Two new global bifurcation theorems and their applications

报告人：代国伟

报告时间：2024年1月20日（周六）上午

报告地点：20-200

报告摘要：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。以第一或通讯作者身份完成SCI论文60余篇，所发表论文被引用590余次。在科学出版社出版专著1部。主持完成两项国家自然科学基金，正在承担国家自然科学基金1项(面上项目)。入选大连理工大学“星海学者”人才培育计划——“星海优青”工程。获省自然科学二等奖1次，高校科技进步一等奖3次、二等奖1次，辽宁省自然科学学术成果二等奖1次。2017年被评为数学物理学报优秀审稿人。

报告题目2：Sharp criteria for nonlocal elliptic inequalities on manifolds

报告人：孙玉华

报告时间：2024年1月20日（周六）上午

报告地点：20-200

报告摘要：We investigate the existence and nonexistence to nonlocal differential inequalities on manifolds. This talk is based on joint work with Qingsong Gu, and Xueping Huang.

报告人简介：孙玉华，南开大学数学学院副教授，博士生导师，研究方向为黎曼流形及图上的分析，包括椭圆及抛物方程，在包括CPAM，JFA, Math. Ann, JAM, CVPDE等著名期刊发表学术论文20余篇。曾获得天津市数学会与统计学联合学术年会“青年学者奖”，南开大学尚格奖教金等荣誉。目前主持国家自然科学基金面上项目一项。

报告题目3：Bubbling Solutions to Lane-Emden Systems

报告人：郭青

报告时间：2024年1月20日（周六）上午

报告地点：20-308

报告摘要：Lane-Emden systems constitute a typical class of Hamiltonian systems, featuring a linear operator with strong indefinite properties and nonlinear terms exhibiting strong coupling characteristics. These inherent properties have presented considerable challenges when applying classical variational methods. We primarily talk on the research works related to the construction of various types of bubbling solutions for critical or supercritical problems using the Lyapunov-Schmidt reduction method. Additionally, we delve into non-degeneracy results by employing local Pohozaev identity techniques. The report is based on joint work with Professor Shuangjie Peng and his doctoral student Liu.

报告人简介：郭青，中央民族大学理学院副教授。2012年博士毕业于中国科学院数学与系统科学研究院，师从曹道民研究员。主要研究方向为非线性偏微分方程中的色散波方程及其稳态问题对应的椭圆型问题。在包括CPDE、JDE、CVPDE、ASNPCS在内的国际学术期刊上发表SCI学术论文二十余篇。主持了三项国家自然科学基金项目。

报告题目4：Partially localized sign-changing solutions for nonlinear elliptic equation

报告人：帅伟

报告时间：2024年1月20日（周六）上午

报告地点：20-308

报告摘要：In this talk, we discuss sign-changing partially localized solutions to the following nonlinear elliptic equation  \begin{equation*}   -\Delta_x v -v_{yy}+q v= |v|^{p-2}v, \ \ (x,y)\in {\R}^N\times{\R},  \end{equation*}  where $N\geq 2$, $q\in {\R}$ and $p\in (2,2^*)$. By partially localized solutions, we refer to solutions $v(x,y)$ that decay to zero as $|x|\rightarrow \infty$ uniformly in $y$. Our main focus is on the existence of sign-changing partially localized solutions that exhibit periodicity in $y$. These solutions are bounded, vanishing on several helicoids and possess a spiraling behavior, meaning that they are not axially symmetric but remain invariant under screw motion.

报告人简介：帅伟，理学博士，华中师范大学副教授。2016年博士毕业于华中师范大学，师从邓引斌教授。2016.12-2018.12 香港中文大学数学科学研究所 助理研究员 合作导师为辛周平教授。主要研究方向是非线性椭圆型偏微分方程、非线性泛函分析。主要成果发表在J. Funct. Anal., Calc. Var. Partial Differential Equations, J. Differential Equations等国际期刊上。现主持青年和面上2项国家自然科学基金。

报告题目5：Reduction, Pohozaev identity and Green’s function

报告人：罗鹏教授

报告时间：2024年1月20日（周六）上午

报告地点：20-202

报告摘要：In this talk, we will introduce some basic methods based on Reduction, Pohozaev identity and Green’s function. And then we give some applications of these methods on the nonlinear elliptic equations without compactness. This talk is based on some jointed work with Prof. Daomin Cao, Massimo Grossi, Shuangjie Peng and Shusen Yan.

报告人简介：罗鹏，华中师范大学教授，博士生导师，2014年于武汉大学获博士学位。研究方向为非线性泛函分析、偏微分方程。主要成果包括：与合作者建立了基于局部Pohozeav恒等式的爆破分析方法，给出了Brezis-Nirenberg问题、Lane-Emden问题正解的非退化性、局部唯一性以及正解的准确数量和Morse指标刻画；与合作者建立了基于Green函数的扰动方法，给出了某些非凸区域上Robin函数和Kirchhoff-Routh函数临界点的个数和非退化性的完整刻画。主要论文发表于J. Eur. Math. Soc.、J. Math. Pures Appl.、Trans. Amer. Math. Soc.等学术期刊。

报告题目6：On sharp discrete Hardy-Rellich inequalities

报告人：黄侠副教授

报告时间：2024年1月20日（周六）上午

报告地点：20-404

报告摘要：Although the history of Hardy inequalities found its origin somehow in the discrete setting, the discrete Hardy-Rellich inequalities are much less understood comparing to the continuous situation. We will show discrete Hardy-Rellich inequalities on $N$ with $\Delta^{k/2}$ and optimal constants for any $k\geq1$. Our approach is to establish some sharp first order Hardy inequalities using weighted equality, and then to handle the higher order cases by iteration. We provide also a first order Leray type inequality on  with the same constants as the continuous setting. The main idea to get weighted equalities works also for general graphs. This is a joint work with Professor Dong Ye at ECNU.

报告人简介：黄侠，副教授，华东师范大学。主要研究来源于几何及物理等学科中的非线性偏微分方程，特别是高阶椭圆型方程。在解的对称性、渐近性、稳定性及解的分类等方面得到一些有意义的研究成果，相关工作发表在JFA、CVPDE、JAM、Nonlinearity、JDE、CRAS等期刊。主持博士后基金一等资助，国家自然科学基金青年项目，面上项目。

报告题目7：Nonlinear elliptic equations of sublinearity: qualitative behavior of solutions

报告人：张程翔副教授

报告时间：2024年1月20日（周六）上午

报告地点：20-404

报告摘要：We study existence, uniqueness and qualitative property of solutions for a class of nonlinear elliptic equations of sublinearity. We also study the asymptotic behavior of ground state solution for sublinear equations in  and give estimates for radius of its support set as various parameters involved including the sublinearity power approaching to the limiting cases. This is a joint work with Profs. Norihisa Ikoma, Kazunaga Tanaka, and Zhi-Qiang Wang.

报告人简介：张程翔，北京师范大学数学科学学院副教授，主要研究方向为偏微分方程和非线性泛函分析，已在ARMA，CVPDE，J. Math. Pures Appl.Indiana Univ. Math. J.等国际知名学术期刊上发表多篇学术论文。主持国家自然科学基金青年项目1项。

报告题目8：Localization analysis of incompressible 3D Navier-Stokes equation and self-similar solutions

报告人：赖柏顺教授

报告时间：2024年1月20日（周六）上午

报告地点：20-200

报告摘要：本报告主要介绍“靠近初始时刻空间局部光滑效应”和频率空间的局部化”的两种局部化技巧，以及这些局部化分析在自相似大解的构造，可能奇点形成必要条件的量化分析等问题方面取得的一些最新进展。同时介绍我们在自相似大解构造方面得到一些结果。

报告人简介：赖柏顺，湖南师范大学数学与统计学院教授，博士生导师，第14届中国数学会理事，长期从事偏微分方程得理论研究，其主要研究领域为不可压缩 Navier-Stokes 方程的数学理论，椭圆方程解的渐近性态、稳定性，其主要成果发表在 Comm. Math. Phys，Adv. Math.，Trans. Amer. Math. Soc.，Sci. China Math.等国内外重要期刊上。

报告题目9：Minimal period problems in Hamiltonian systems

报告人：张端智教授

报告时间：2024年1月20日（周六）上午

报告地点：20-202

报告摘要：In this talk, we consider the minimal period problems in Hamiltonian systems. Applying the Maslov-type index theory, we will give some estimates for the minimal period or minimal symmetric period of symmetric periodsolutions including brake orbits, P-symmetric period solutions, and P-symmetric brake orbits in C2 Hamiltonian systems with corresponding symmetry. We will also consider non C2 case for n=1.

报告人简介：张端智，南开大学数学科学学院教授、博士生导师，中国数学会非线性泛函分析专业委员会委员，主持国家自然科学基金和国家重点研发课题多项。主要从事非线性分析与辛几何，哈密顿系统指标理论的研究，在哈密顿系统周期解的多重性与稳定性以及最小周期等相关问题的研究中取得进展。相关研究成果发表在Comm. Pure Appl. Math.，Adv. Math, Proc. LMS, Ann. Inst. H. Poincare. Anal. Nonlineire, Calc. Var. PDE, JDE等重要数学期刊上。

报告题目10：Mean field equation and its applications in Trudinger-Moser type inequalities

报告人：胡烨耀副教授

报告时间：2024年1月20日（周六）上午

报告地点：20-202

报告摘要：In this talk, we will first review the resolution of the celebrated Chang-Yang conjecture on a sharp Trudinger-Moser type inequality on the two-dimensional sphere. Then higher dimensional analogues will be presented and some very recent progress will be introduced. We will also mention some related open problems that the audience might be interested in.

报告人简介：胡烨耀，中南大学数学与统计学院特聘副教授，博士生导师。主要从事椭圆型偏微分方程与共形几何等方向的研究。获浙江大学数学学士和美国乔治华盛顿大学博士学位，之后在美国得克萨斯大学圣安东尼奥分校担任博士后研究员。其研究成果在 《J. Funct. Anal.》、《Int. Math. Res. Not. IMRN》、《SIAM J. Math. Anal.》、《Calc. Var. Partial Differential Equations》、《J. Differential Equations》、《Nonlinearity》等权威期刊上发表。

报告题目11：约束变分方法及其在Schrödinger-Poisson方程中的应用

报告人：贺小明教授，中央民族大学

报告时间：2024年1月20日（周六）下午

报告地点：20-202

报告摘要：本报告围绕约束变分问题，先概述约束变分问题的历史、研究现状和最新研究进展；然后针对几类具有临界指数增长的Schrödinger-Poisson方程，讨论其规范化解的存在性和相关问题。

报告人简介：贺小明教授， 理学博士，美国数学会数学评论评论员，德国数学文摘评论员， 中央民族大学应用数学研究所所长。近年来，在非局部椭圆型微分方程解的存在性，多解性，集中性以及规范化解的存在性等方面取得了若干研究成果，引发了许多后续的研究工作。已在国内外数学期刊，如Manuscript. Math.， Calc. Var. PDE，J. Geometric Analysis， J. Differential Equations，Ann. Mat. Pura Appl.，Nonlinearity等上发表科研论文七十多篇，被他人SCI引用1800多次。自2009年来，连续四次获得国家自然科学基金面上项目资助。

报告题目12：Classification of solutions for some higher order elliptic equations in half space

报告人：余晓辉教授，深圳大学

报告时间：2024年1月20日（周六）下午

报告地点：20-202

报告摘要：In this talk, I will introduce some classification results for higher order elliptic equations in half space. Under some assumptions, we write out the solution explicitly on the boundary of the half space. However, we don’t know the expressions of the solutions on half space, this is different from the second order problem.

报告人简介：余晓辉，深圳大学数学与统计学院教授，研究领域为非线性偏微分方程。近年来在国际著名学术期刊如Calculus of Variations and PDE, Journal of Functional Analysis, Journal of Differential Equations等学术期刊上发表论文三十余篇，主持国家自然科学基金5项。2012年当选为深圳大学首届优秀青年教师。

报告题目13：Riccati-type inequalities and blow-up analysis of solutions to some equations

报告人：魏龙副教授，杭州电子科技大学

报告时间：2024年1月20日（周六）下午

报告地点：20-200

报告摘要：In this talk, we investigate blow-up phenomena of solutions to some equations by Riccati-type inequalities. This method provides the possibility of discovering new blow-up criteria. Our conclusions suggest that the blow up for the solutions may occur even with small slope of the initial data.

报告人简介：魏龙，男，江苏人， 2007年于华东师范大学数学系博士毕业。目前主要研究感兴趣于半线性椭圆方程解的集中现象、全空间解的渐近性态，非线性色散波方程的适定性、解的爆破分析、衰减持续性等，已在J. Differential Equations，J. Dyn. Differ. Equ.，Discrete Contin. Dyn. Syst.(-A,-B), Adv. Nonlinear Stud.，J. Math. Phys., Pacific J. Math., Nonlinear Differ. Equ. Appl., Comm. Pure Appl. Anal., Adv. Differ. Eqs.等杂志上发表论文40余篇。

报告题目14：Semi-classical limit of Gross-Pitaevskii equations

报告人：高琦副教授，武汉理工大学

报告时间：2024年1月20日（周六）下午

报告地点：20-200

报告摘要：In this talk, I will present some results on the semiclassical limit for Gross-Pitaevskii equations in an exterior domain with different settings. This is a joint work with Chiun-Chang Lee and Tai-Chia Lin.

报告人简介：高琦，武汉理工大学数学系副教授，加拿大McMaster University获得博士学位。主要研究兴趣为非线性偏微分方程以及应用，国家青年基金项目主持人。主要研究结果发表在JDE，JFA，ZAMP等国际学术期刊上。

报告题目15：Some properties of generalized singular integrals

报告人：陈艳萍教授，北京科技大学

报告时间：2024年1月20日（周六）下午

报告地点：20-404

报告摘要：This talk is concerned with the generalized singular integral operator and the application for the generalized surface quasi-geostrophic equation.

报告人简介：陈艳萍，北京科技大学数理学院副院长，教授，博士生导师。2007年博士毕业于北京师范大学。2009年获得全国优秀博士学位论文提名奖，获2022年度教育部高等学校科学研究优秀成果奖自然科学二等奖（排第一）。主要研究方向为调和分析及其应用，并主持和参加多项国家自然科学基金。在Anal. and PDE、Trans. Amer. Math. Soc.、J. Funct. Anal.、Rev. Mat. Iberoam.等国内外知名杂志上发表学术论文多篇。

报告题目16：Normalized ground states for a coupled Schrödinger system

报告人：张建军教授，重庆交通大学

报告时间：2024年1月20日（周六）下午

报告地点：20-404

报告摘要：In this talk, we are concerned with the existence of normalized solutions to systems of coupled Schr\odinger equations$$\left\lbrace\begin{aligned}-\Delta u+\lambda_{1}u&=\mu_{1}u^{p-1}+\beta r_{1}u^{r_{1}-1}v^{r_{2}},\\-\Delta v+\lambda_{2}v&=\mu_{2}v^{q-1}+\beta r_{2}u^{r_{1}}v^{r_{2}-1},\\0<u,v\in &H^{1}(\mathbb{R}^{n}), \ \ 1\leq N\leq4.\end{aligned}\right. $$satisfying the normalization$$\int_{\mathbb{R}^{n}}u^{2}dx=a,\ \ \int_{\mathbb{R}^{n}}v^{2}dx=b.$$Here $\mu_{1}$, $\mu_{2}$, $\beta>0$ and the prescribed masses $a,b>0$. We focus on the coupled purely mass super-critical case, i.e.,$$2+\frac{4}{N}<p,q, r_{1}+r_{2}<2^{*}$$ with $2^{*}$ being the Sobolev critical exponent. We optimize the range of $(a,b,\beta, r_{1},r_{2})$ for the existence. In particular, for $N=3,4$ with $r_{1},r_{2}\in(1,2)$ our result indicates the existence for all $a,b>0$ and $\beta>0$. This is based on the joint work with Louis Jeanjean and Xuexiu Zhong.

报告人简介：张建军，重庆交通大学数学与统计学院教授，重庆市数学会副理事长，贵州大学博士生导师。2001年本科毕业于中国矿业大学数学系，2012年于清华大学数学科学系获博士学位，2018年获得意大利副教授国家资格认证，2020年入选重庆市高校中青年骨干教师，主持国家自然科学基金3项和意大利伦巴第研究员基金（Global ERC）各1项。在非线性薛定谔方程的半经典状态和规范化解的研究等方面取得了一些结果，在JMPA，CPDE，CVPDE，JDE，Nonlinearity等刊物上发表多篇论文。

报告题目17：Stability of the Caffarelli-Kohn-Nirenberg inequality: the existence of minimizers

报告人：吴元泽教授，中国矿业大学

报告时间：2024年1月20日（周六）下午

报告地点：20-306

报告摘要：In this paper, we consider the following variational problem:$$\inf_{u\in D^{1,2}_a(\mathbf{R}^N)\backslash\mathcal{Z}}\frac{\|u\|^2_{D^{1,2}_a(\mathbb{R}^N)}-C_{a,b,N}^{-1}\|u\|^2_{L^{p+1}(|x|^{-b(p+1)},\mathbb{R}^N)}}{dist_{D^{1,2}_{a}}^2(u, \mathcal{Z})}: =c_{BE},$$where$N\geq2$, $b_{FS}(a)<b<a+1$ for $a<0$ and $a\leq b<a+1$ for $0\leq a<a_c:=\frac{N-2}{2}$ and $a+b>0$ with $b_{FS}(a)$ being the Felli-Schneider curve, $p=\frac{N+2(1+a-b)}{N-2(1+a-b)}$, $\mathcal{Z}= \{ c \tau^{a_c-a}W(\tau x)\mid c\in\mathbb{R}\backslash\{0\}, \tau>0\}$ and up to dilations and scalar multiplications, $W(x)$, which is positive and radially symmetric, is the unique extremal function of the following classical Caffarelli-Kohn-Nirenberg (CKN for short) inequality $$\bigg(\int_{\mathbb{R}^N}|x|^{-b(p+1)}|u|^{p+1}dx\bigg)^{\frac{2}{p+1}}\leq C_{a,b,N}\int_{\mathbb{R}^N}|x|^{-2a}|\nabla u|^2dx$$ with $C_{a,b,N}$ being the optimal constant.  It is known in [J. Wei-Y. Wu, MAAN, 2022] that $c_{BE}>0$.  In this paper, we prove that the above variational problem has a minimizer for $N\geq2$ under the following two assumptions:\item[$(i)$]\quad $a_c^*\leq a<a_c$ and $a\leq b<a+1$,  \item[$(ii)$]\quad $a<a_c^*$ and $b_{FS}^*(a)\leq b<a+1$,where $a_c^*=\bigg(1-\sqrt{\frac{N-1}{2N}}\bigg)a_c$ and $$b_{FS}^*(a)=\frac{(a_c-a)N}{a_c-a+\sqrt{(a_c-a)^2+N-1}}+a-a_c.$$ Our results extend that of Konig in [T. Konig, JEMS, 2023] for the Sobolev inequality to the CKN inequality.  Moreover, we believe that our assumptions~$(i)$ and $(ii)$ are optimal for the existence of minimizers of the above variational problem.

报告人简介：吴元泽，博士、中国矿业大学青年学术带头人、教授、博士生导师，数学系科研副主任。兼任第十三届江苏省数学会理事、美国数学会《Mathmatical Reviews》评论员。获第八届江苏省数学成就奖。主要研究领域为非线性分析和非线性椭圆型偏微分方程（组）。现主持国家自然科学基金面上项目一项，主持完成国家自然科学基金青年基金、数学天元基金各1项。发表学术论文近30篇，其中部分成果发表于《Math. Ann.》，《J. Math. Pures Appl.》，《J. Funct. Anal.》，《Calc. Var. PDEs》，《Nonlinearity》等学术刊物上。

报告题目18：非局部临界问题的高能量解

报告人：王大斌教授，汕头大学

报告时间：2024年1月20日（周六）下午

报告地点：20-306

报告摘要：利用度理论，全局紧等变分方法研究几类非局部问题高能量解的存在性和多解性。

报告人简介：王大斌，理学博士，汕头大学教授，硕士生导师。曾在华中师范大学从事博士后研究工作，主要研究方向是非线性泛函分析、非线性椭圆型偏微分方程。主要成果发表在Journal of Differential Equations、Journal of Geometric Analysis，Communications in Contemporary Mathematics，Journal of Mathematical Physics等国际数学期刊上。现主持2项国家自然科学基金项目。

报告题目19：Infinitely many dichotomous type peak solutions for singularly perturbed Schrodinger equations

报告人：龙薇教授，江西师范大学

报告时间：2024年1月20日（周六）下午

报告地点：20-308

报告摘要：This talk is mainly concerned with the existence of peak solutions for a singularly perturbed Schrodinger equations. We apply non-degeneracy of the ground state solution for the above equation to construct infinitely many solutions with peaks locating both in the bounded domain and near infinity.

报告人简介：龙薇，女，教授、博士生导师，主要从事偏微分方程与非线性分析的研究。近年来，在Ann. Sc. Norm. Super. Pisa Cl. Sci.、J. Differential Equations、Proc. Roy. Soc. Edinburgh Sect. A等国际权威期刊发表学术论文40多篇；承担了多项国家自然科学基金的研究（主持面上和青年项目各1项）；获省自然科学奖二等奖、省高校科技成果奖一等奖各1次；担任了美国数学评论和德国数学文摘评论员；指导的学生多人获国家奖学金、省政府奖学金、省优秀硕士学位论文、数学建模竞赛奖等荣誉。

报告题目20：On Soave's open problems for nonlinear Schr\odinger equations with general nonlinearities and Sobolev critical exponents

报告人：钟学秀副研究员，华南师范大学

报告时间：2024年1月20日（周六）下午

报告地点：20-308

报告摘要：We study the existence, multiplicity of prescribed mass positive solutions to a Schr\odinger equation of the form$$-\Delta u-\lambda u=f(u), u\in H^1(\R^N), N\geq 3,$$  where $f\in C(\R,\R)$ is a very general nonlinearity having a Sobolev critical growth. We mainly study the pure mass supercritical case and the mass mixed critical case. Precisely, for the pure mass supercritical case, under related mild assumptions, we establish the existence of mountain pass normalized solution for all prescribed mass $c>0$. We also capture its precise asymptotic behavior as $c\rightarrow 0^+$ as well as $c\rightarrow +\infty$. For the mass mixed case, we can find at least two different positive normalized solutions for small $c>0$. One is a local minimizer and the other one is a mountain pass solution. We also establish a sequence of properties for the local minimizer including the uniqueness, asymptotic behavior,etc. The asymptotic behavior of the mountain pass solution as $c\rightarrow 0^+$ is also studied. Our results solve a sequence of open problems proposed by Soave ({\em J. Funct. Anal.}, 279(6):108610, 2020).

This is a joint work with Vicentiu D. Radulescu,Jianjun Zhang and Jinfang Zhou.

报告人简介：钟学秀，华南师范大学副研究员。研究方向为运用非线性分析、变分法等方法来研究几何分析学、数学物理中椭圆型偏微分方程和方程组以及某些不等式问题。主持国家青年基金和面上基金各一项。已在J.Differential Geom.， Math. Ann.， J. Math. Pures Appl.， Ann. Sc. Norm. Super. Pisa Cl. Sci. ，Calc. Var. PDE，J. Differential Equations等国际重要刊物上发表多篇学术论文。在非线性泛函分析和椭圆偏微分方程领域的Li-Lin公开问题，Sirakov公开问题，Bartsch-Jeanjean-Soave公开问题等方面获得了重要进展。

报告题目21：Method of scaling spheres: Liouville theorems in general bounded or unbounded domains, blowing-up analysis on non-$C^1$ domains and other applications

报告人：戴蔚教授，北京航空航天大学

报告时间：2024年1月21日（周日）上午

报告地点：20-202

报告摘要：In this talk, we aim to introduce the method of scaling spheres (MSS) as a unified approach to Liouville theorems on general domains and apply it to establish Liouville theorems on arbitrary unbounded or bounded MSS applicable domains for general $\leq n$-th order PDEs and integral equations without translation invariance or with singularities. The set of MSS applicable domains includes any unbounded or bounded generalized radially convex domains and any complementary sets of their closures, which is invariant under Kelvin transforms and is the maximal collection of domains such that the MSS works. For instance, $\mathbb{R}^{n}$, $\mathbb{R}^{n}_{+}$, balls, bounded or unbounded cone-like domains, exterior domains, convex domains, star-shaped domains and all the complements of their closures are MSS applicable domains. One should note that, MSS applicable domains is to the MSS what convex domains (at least in one direction) is to the famous method of moving planes. As applications, we derive a priori estimates and hence existence of positive solutions from the boundary Hölder estimates for ≤n-th order elliptic equations by applying the blowing-up argument on domains with blowing-up cone boundary (BCB domains for short). After the blowing-up procedure, the BCB domains allow the limiting shape of the domain to be a cone (half space is a cone). While the classical blowing-up techniques in previous works work on $C^1$-smooth domains, we are able to apply blowing-up analysis on more general BCB domains on which the boundary Holder estimates hold (can be guaranteed by uniform exterior cone property etc).

报告人简介：戴蔚，北京航空航天大学数学科学学院教授，基础数学系主任，博士生导师。2012年博士毕业于中国科学院数学与系统科学研究院，曾赴美国UC Berkeley与法国Universite Sorbonne Paris Nord做访问学者。主持国家自然科学基金3项。主要研究分数阶与高阶椭圆方程、发展方程及调和分析。相关研究结果发表在Adv. Math.、Trans. AMS、JFA、CVPDE等国际数学权威期刊上。

报告题目22：A discrete data assimilation algorithm for the three dimensional planetary geostrophic equations of large-scale ocean circulation

报告人：尤波教授，西安交通大学

报告时间：2024年1月21日（周日）上午

报告地点：20-202

报告摘要：In this talk, we consider a discrete data assimilation algorithm for the three dimensional planetary geostrophic equations of large-scale ocean circulation in the case that the observable measurements, obtained discretely in time, may be contaminated by systematic errors, which works for a general class of observable measurements, such as low Fourier modes and local spatial averages over finite volume elements. We will provide some suitable conditions to establish asymptotic in time estimates of the difference between the approximating solution and the unknown exact (reference) solution in some appropriate norms for these two different kinds of interpolant operators, which also shows that the approximation solution of the proposed discrete data assimilation algorithm will convergent to the unique unknown exact solution of the original system at an exponential rate, asymptotically in time if the observational measurements are free of error.

报告人简介：尤波，西安交通大学数学与统计学院教授、博士生导师，2012年毕业于兰州大学，2014年9月-2015年9月曾访问美国佛罗里达州立大学。主要研究领域为非线性泛函分析与无穷维动力系统。迄今为止，已在JDDE,AMO,NA,ZAMP,CMS,DCDS等杂志发表学术论文40余篇。曾主持完成四项国家和省部级科研项目。目前，主持一项国家自然科学基金面上项目。

报告题目23：On uniqueness of multi-bubble blow-up solutions and multi-solitons to L^2-critical NLS

报告人：苏一鸣副教授，浙江工业大学

报告时间：2024年1月21日（周日）上午

报告地点：20-200

报告摘要：We are concerned with the focusing L^2-critical nonlinear Schrodinger equations. The uniqueness is proved for a large energy class of multi-bubble blow-up solutions, which converge to a sum of K pseudo-conformal blow-up solutions particularly with the low rate (T-t)^{0+}. Moreover, we also prove the uniqueness in the energy class of multi-solitons which converge to a sum of K solitary waves with convergence rate (1/t)^{2+}. The uniqueness class is further enlarged to contain the multi-solitons with even lower convergence rate (1/t)^{1/2+} in the pseudo-conformal space.

报告人简介：苏一鸣，2014年在中国科学院数学与系统科学研究院获博士学位，现为浙江工业大学理学院副教授。研究方向主要为偏微分方程，特别是在非线性Schrödinger方程取得重要进展，在 ARMA、J. Funct. Anal. 等期刊上发表高水平论文多篇。主持完成国家自然科学基金青年项目等多项课题。

报告题目24：Existence and qualitative properties of solutions to planar Choquard system in the Sobolev limiting case

报告人：刘志苏教授，中国地质大学

报告时间：2024年1月21日（周日）上午

报告地点：20-200

报告摘要：In this report, we introduce the nonlinear Choquard equation in the Sobolev limiting case. We prove existence of solutions by means of a variational approximating procedure for an auxiliary Choquard equation in which the uniformly approximated sign-changing logarithmic kernel competes with the exponential nonlinearity. Qualitative properties of solutions such as symmetry and decay are also established by exploiting a suitable moving planes technique.

报告人简介：刘志苏，湖南大学博士，中国地质大学（武汉）特任教授。研究方向是非局部椭圆偏微分方程中的变分问题以及多智能体系统的集群稳定性问题。主持国家自然科学基金青年、天元、天元访问各一项。获湖南省自然科学一等奖、三等奖各1项（第四完成人）。在国内外学术刊物上发表论文40余篇，部分研究成果发表在 CVPDE, Nonlinearity, JDE, Israel J. Math, AMPA等刊物上。现为德国Zentralblatt MATH 评论员，美国数学评论员，国际差分方程协会会员。

报告题目25：Some results about the weighted fourth order elliptic problems

报告人：邓圣兵教授，西南大学

报告时间：2024年1月21日（周日）上午

报告地点：20-404

报告摘要：In this talk, I will introduce some recently results about the weighted fourth order elliptic problems, which includes the existence of the sharp constants and optimizers for the weighted Caffarelli Kohn Nirenberg type inequalities, and the classification and non-degenerate of the solutions for some weighted equations. As an application, we will consider the remainder term of some CKN type inequalities.

报告人简介：邓圣兵，西南大学数学与统计学院教授，博士生导师。2013年于智利大学获博士学位，2014年8月起在西南大学数学与统计学院工作。主要研究领域为非线性泛函分析、偏微分方程及其应用，在椭圆型方程解的存在性、多解性与解的集中现象等方面做出了很多重要的研究工作，在Proc. London Math. Soc、J. Funct. Anal.、J. Differential Equations、Comm. Anal. Geom、Int. Math. Res. Not.、Math.Z.等期刊上发表论文40余篇，主持国家自然科学基金项目3项。

报告题目26：Existence and blow up behavior of positive normalized solution to the Kirchhoff equation with general nonlinearities

报告人：张贻民教授，武汉理工大学

报告时间：2024年1月21日（周日）上午

报告地点：20-404

报告摘要：In present talk, I will give the existence of normalized solutions to Kirchhoff problem satisfying the normalization constraint conditions which appears in free vibrations of elastic strings. The nonlinearities considered here are very general and of mass super-critical. Under some suitable assumptions, we can prove the existence of ground state normalized solutions for any given mass. After a detailed analysis via the blow up method, we also make clear the asymptotic behavior of these solutions.

报告人简介：张贻民，男，2003年四川大学数学科学学院本科毕业，2009年华南理工大学获得理学博士学位，2010年至2012年在中国科学院武汉物理与数学研究所从事博士后研究工作，2012年至2016年任中国科学院武汉物理与数学研究所副研究员，2016年起任武汉理工大学教授，博士生导师。主要研究方向为非线性泛函分析和非线性偏微分方程。

报告题目27：On location of maximal gradient of torsion function and related problems

报告人：李沁峰副教授，湖南大学

报告时间：2024年1月21日（周日）上午

报告地点：20-306

报告摘要：We study the classical torsion problem on convex domains, focusing on determining the location of maximal gradient of torsion function, which physically means maximal stress of material. A long-standing belief, which is the modified Saint-Venant conjecture, states that for an evenly symmetric convex domain, points of maximal stress must be either on the shorter axis or location of minimal curvature. We disprove this folklore via domain variational approach and harmonic extension argument. Nevertheless, we prove that the original Saint-Venant’s conjecture is valid if the domain is sufficiently narrow. Moreover, for triangles and rectangles, we can exactly determine the position at which maximal stress occurs, and we also prove uniqueness and nondegeneracy of critical points on each side, via moving plane method and nodal line analysis. Open questions will be given along the talk.

报告人简介：李沁峰，2018年博士毕业于普渡大学，之后在德州大学圣安东尼奥分校做博士后研究，2020年8月至今在湖南大学工作。主要研究方向是几何测度论、区域变分问题以及非线性偏微分方程，文章发表在IMRN, CVPDE, IUMJ, Adv. CV等杂志上。

报告题目28：Long-time dynamics of a nonlocal diffusion model with free boundaries in high dimensions

报告人：倪文杰副教授，新英格兰大学

报告时间：2024年1月21日（周日）上午

报告地点：20-306

报告摘要：In this talk, I will report some results about a kind of nonlocal diffusion equation with free boundaries in high dimensions. Professor Du and his collaborators introduced and studied a nonlocal diffusion problem with free boundary condition in one dimension space. It was shown that a spreading-vanishing dichotomy holds, and the speed of the spreading front is determined by a semi-wave problem, where infinite speed (accelerated spreading) is possible. For kernel functions that behave like a polynomial function near infinity, Professor Du and me obtain better estimates of the spreading speed for both the finite speed case, and the infinite speed case. We also studied the spreading speed in high dimensions.

报告人简介：倪文杰，澳大利亚新英格兰大学博士后。2018年7月获得哈尔滨工业大学基础数学博士学位。2016/09-2018/02作为联合培养博士研究生赴美国威廉玛丽学院学习。现为澳大利亚新英格兰大学数学系博士后。在CVPDE, JDE, Nonlinearity, Proceedings of AMS 等数学期刊发表数篇文章。主要研究方向为反应扩散方程与自由边界问题解的长时间行为。

报告题目29：Lazer-Mckenna Conjecture for fractional problems involving critical growth

报告人：李本鸟副教授，江西师范大学

报告时间：2024年1月21日（周日）上午

报告地点：20-308

报告摘要：In this talk, I will introduce some results on the fractional critical elliptic problem with Ambrosetti-Prodi type, which is related to Lazer-McKenna conjecture. In this work, we have constructed bubbling solutions when the parameter is large enough, and the location of the bubbling point is near the boundary of the domain. This work is joint with Wei Long and Zhongwei Tang.

报告人简介：李本鸟，博士毕业于澳大利亚新英格兰大学, 之后在澳大利亚新英格兰大学做博士后研究；主要研究二阶椭圆方程解的存在性和唯一性问题，在Calculus of Variations and Partial Differential Equations，Journal of Differential Equations，Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V等国际知名数学期刊上发表多篇高水平论文。

邀请人：非线性分析与PDE团队