活动地点: Tencent会议 383-6526-3579

题目: Well-posedness and strong attractors for a beam model with degenerate nonlocal strong damping,

活动内容摘要: In this talk, we consider the initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in a bounded domain. We prove the global existence and uniqueness of weak solutions and establish the existence of a strong attractor for the corresponding weak solution semigroup, where the “strong” means that the compactness and attractiveness of the attractor are in the topology of a stronger phase space.,

时间: 2023-06-17 08:00,

主讲人: 钟承奎,

主讲人简介: 钟承奎, 南京大学数学系教授、博士生导师。长期从事非线性泛函分析与无穷维动力系统的研究，其中在无穷维动力系统全局吸引子问题的研究中取得了一系列深入的理论和应用性研究成 果。在非线性泛函分析领域中，关于 Ekeland 变分原理、乘积空间上的指标理论以及带有凸凹非线性项的半线性椭圆型方程的研究中，取得了重要的研究成果。于1998年获得了甘肃省科技进步二等奖，2007年获得了甘肃省自然科学一等奖，多次参加和主持国家 自然科学基金面上项目，重点项目及教育部重点项目。,

题目: Dynamics of helical flows of Maxwell fluids,

活动内容摘要: Helical flows of Maxwell fluids can be reduced to a system of two wave equations with non-homogeneous coefficients. In this talk we shall establish some results concerning longtime dynamics of such flows.,

时间: 2023-06-17 08:45,

主讲人: Ma To Fu,

主讲人简介: To Fu Ma，巴西利亚大学终身教授，博士生导师，数学系副主任。曾任巴西圣保罗大学（圣卡洛斯大学）数学与计算机科学研究所（ICMC）教授，主要研究偏微分方程及无穷维动力系统，1998 年获葡萄牙里斯本大学博士学位，主持和完成多项巴西国家自然科学基金项目，在数学核心期刊上发表论文70 余篇，他引1500 多次，先后30 余次国际学术会议上作学术报告，培养20 余名博士和博士后人员。,

题目: Statistical solutions and Liouville theorem for the Klein-Gordon-SchrÖdinger equations,

活动内容摘要: In this talk, we investigate the system of SchrÖdinger and Klein-Gordon equations with Yukawa coupling. They first prove the existence of pullback attractor and construct a family of invariant Borel probability measures. Then they establish that this family of probability measures satisfies a Liouville type theorem and is indeed a statistical solution for the coupling equations. Further, they reveal that the invariant property of the statistical solution is a particular situation of the Liouville type theorem.  This work is jointly with T. Caraballo and G. Lukaszewicz.,

时间: 2023-06-17 09:30,

主讲人: 赵才地,

主讲人简介: 赵才地，温州大学瓯江特聘教授，温州市科技创新领军人才，浙江省新世纪151人才。主要从事无穷维动力系统与非线性偏微分方程方面的研究工作。 应用无穷维动力系统的途径研究非线性发展方程的不变测度和统计解，在一些典型偏微分方程的统计解、轨道统计解，以及随机偏微分方程的不变样本测度等方面取得一些成果，在Advances in Differential Equations，Nonlinearity，J. Differential Equations, 《中国科学》等期刊上发表学术论文50余篇，曾获浙江省自然科学三等奖。,

题目: Global attractor of subcritical 2D vorticity Boussinesq equations,

活动内容摘要: In this talk, we consider the subcritical Boussinesq system with fractional dissipation in T^2. Our aim is to study the long-time behavior of solutions of Boussinesq system in its natural scale-invariant Sobolev space and prove the existence of a global attractor of optimal regularity. To this end we investigate the global well-posedness and global attractor for Boussinesq system in H^(2-α) (T^2)×H^(2-α) (T^2) via commutator estimates for nonlinear terms and a new energy estimate in Sobolev spaces to bootstrap the regularity, derived by means of nonlinear lower bounds on the fractional Laplacian. Besides, we study the upper semicontinuity when α→1^+.,

时间: 2023-06-17 10:30,

主讲人: 岳高成,

主讲人简介: 岳高成，2010年毕业于兰州大学，获理学博士学位，现为南京航空航天大学数学学院副教授，硕士生导师。主要从事无穷维动力系统与非线性偏微分方程方面的研究工作。在Appl. Math. Optim.、. Bull. Sci. Math.、 Discrete Contin. Dyn. Syst.、Nonlinear Anal.、 J. Math. Anal. Appl.等期刊上发表多篇论文。,

题目: On a parabolic-elliptic Keller-Segel system with signal-dependent motility,

活动内容摘要: In this talk, we would like to report our recent work on a Keller-Segel system of chemotaxis. The model features signal-dependent motility function, which may vanish as the concentration becomes unbounded, leading to a possible degenerate problem. We develop systematic new methods relying mainly on various comparison techniques to study the existence and boundedness problem. The talk is based on my recent joint works with Kentaro Fujie (Tohoku University), Philippe Laurençot (CNRS and University of Savoie Mont Blanc), Yanyan Zhang (ECNU), and Yamin Xiao (IAPCM).,

时间: 2023-06-17 11:15,

主讲人: 江杰,

主讲人简介: 江杰，中国科学院精密测量科学与技术创新研究院，研究员。2004年毕业于山东大学数学与系统科学学院基地班，2009年于复旦大学数学科学学院获得理学博士学位，师从郑宋穆教授。2009年到2011年在北京应用物理与计算数学研究所郭柏灵院士指导下从事博士后工作。主要研究相场-流体方程、趋化方程等非线性方程整体解的存在唯一性、有界性、渐近性以及无穷维动力系统的性质等。目前在CPDE、CVPDE、JDE、SIMA等国际数学刊物正式发表SCI论文28篇。主持国家自然科学基金面上项目、青年基金等项目。,

题目: Chaos of multi-dimensional linear hyperbolic PDEs,

活动内容摘要: This report deals with the dynamics of a system governed by a multi-dimensional linear hyperbolic PDE. The dynamical behaviors of linear PDEs extremely depend on the selection of space, and a conventional way is to define an infinite-dimensional space with a tuning parameter. Thereby, the linear PDEs can exhibit chaos or stability in the different range of tuning parameter. In this work, the chaos of the C0-semigroup corresponding to the system is established on the Banach space of multivariate analytic functions when the tuning parameter exceeds some given positive number. Based on this, both Devaney and distributional chaos of the system are further obtained. Meanwhile, the C0-semigroup is proved to be uniformly exponentially stable when the tuning parameter is less than a certain positive number, which contributes to showing the global stability of the system. Finally, two examples are given to illustrate effectiveness of our results.,

时间: 2023-06-17 14:00,

主讲人: 杨启贵,

主讲人简介: 杨启贵，二级教授，理学博士，博士生导师，华南理工大学教学名师. 主要从事微分方程几何理论、混沌动力系统、随机动力系统及其应用的研究与教学工作，揭示混沌系统混沌机理与复杂动力学特征. 曾获省部级科技进步一等奖(排名：1\/4)等, 连续3次广东省优秀博士论文指导教师等. 至现今为止，在J. Differential Equations等国内外发表论文140多篇，到目前为止，SCI正面他引2300多次. 主持混沌方面的国家自然基金项目5项、省级自然基金项目6项、国家或省部级教研项目13项, 国家一流专业负责人, 参加国家自然科学基金重大科研仪器研制项目1项、国家自然基金项目4项和省研究团队1项等. 曾多次为国家自然科学奖的会评或通讯评审专家等。,

题目: The uniform asymptotic behavior of solutions for g-Navier-Stokes equations,

活动内容摘要: This talk contains two parts: (1) We consider the long-time behavior of g-Navier-Stokes equations with weak dampness and time delay on bounded domain. the existence of the uniform attractor for the equation is proved with the restriction of the forcing term belonging to translational compacted function space. (2) The uniform asymptotic behavior of solutions for 2D g-Navier-Stokes equations with nonlinear dampness is studied on unbounded domain. The uniform asymptotic properties is proved with the energy equation method and the uniform attractor is obtained. Finally, the dimension of the uniform attractor is estimated in the quasi-periodical case. This talk is based on the joint works with Xiaoxia Wang.,

时间: 2023-06-17 14:45,

主讲人: 姜金平,

主讲人简介: 姜金平，延安大学教授，博士，毕业于西安交通大学计算数学专业，师从侯延仁教授，主要从事非线性发展方程和无穷维动力系统等方面的研究。现为陕西省数学会理事和陕西省工业与应用数学学会理事，延安大学应用数学研究中心主任。在《Applied Mathematics and Computation》，《Applied Mathematics and Mechanics》，《Advances in Applied Mathematics and Mechanics》等期刊发表学术论文60多篇。主持和参与国家自然科学基金、陕西省自然科学基金项目5项，获得陕西省高等学校科学技术奖2项。,

题目: Strongly compact strong trajectory attractors for the nonautonomous 3D Navier-Stokes equations,

活动内容摘要: We show that for any fixed accuracy and time length T, a finite number of T-time length pieces of the complete bounded solutions on the global attractor are capable of uniformly approximating all Leray-Hopf weak solutions within the accuracy in the natural strong metric after sufficiently large time when the 3D Navier-Stokes equations is with a fixed normal force and every complete bounded solution is strongly continuous. Moreover, we obtain the strong equicontinuity of all the complete bounded solutions on the global attractor. These results follow by proving the existence of a strongly compact strong trajectory attractor for such a system. The notion of a (weak) trajectory attractor was previously constructed for a family of auxiliary systems including the originally considered one. We developed a framework called evolutionary system, with which a (weak) trajectory attractor can be actually defined for the original system nearly ten years ago. Very recently, the theory of trajectory attractors is further developed in the natural strong metric for our purpose. The framework is general and can also be applied to other nonautonomous dissipative partial differential equations for which the uniqueness of solutions might not hold.,

时间: 2023-06-17 15:30,

主讲人: 卢松松,

主讲人简介: 卢松松, 中山大学数学学院, 副教授。主要从事耗散发展方程的解的长时间行为的研究, 通过一系列的工作（部分与别人合作）建立了一个理论框架来描述系统的动力学行为, 得到了一类耗散系统的一些有趣的结果。相关结果发表在DCDS-A, JDE, Asymptot. Anal., DCDS S, Adv. Math. 等期刊上。,

题目: Martingale solutions and invariant measures for fractional Navier-Stokes equations on unbounded 3D domains,

活动内容摘要: In this talk, we investigate the stochastic fractional Navier-Stokes equations on unbounded 3D domains. By the Faedo-Galerkin approximation, the compactness method and the Skorokhod’s theorem, we get the existence of martingale solution for the equation. We also show that if the Lipschitz constant L of nonlinear function of random external force term is less than, then the martingale solution is the strong solution in the sense of probability. By this fact, using the weak Feller method, we get the existence of invariant measure for the equation.,

时间: 2023-06-17 16:30,

主讲人: 李晓军,

主讲人简介: 李晓军，河海大学教授，博士生导师。主要从事非线性泛函分析、无穷维动力系统与随机偏微分方程的研究。美国迈阿密大学、美国杨百翰大学访问学者。现为美国《Mathematical Reviews》和德国《Zentralblatt MATH》特邀评论员，已在J. Differential Equations、J. Math. Phys.、Z. Angew. Math. Phys、Bull. Sci. Math.等杂志上发表SCI论文二十余篇，主持国家自然科学基金面上项目2项。,

题目: Existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory,

活动内容摘要: In this talk, I shall report the latest results on the existence and regularity of global attractors for a Kirchhoff wave equation with strong damping and memory in the weighted time-dependent spaces. First of all, we transform the equation under study into a new form. Then, using some prior estimates and energy estimates to the obtained equation, we establish the existence of the absorbing set for the process. After that, we verify the asymptotic compactness of the process by a contraction function and obtain the existence of global attractors. Finally, by decomposing the weak solutions into two parts and some elaborate calculations, we derive the regularity of solutions. This work is jointly with Yuming Qin and Alain Miranville.,

时间: 2023-06-17 17:15,

主讲人: 杨彬,

主讲人简介: 杨彬，2018年研究生推荐免试进入东华大学理学院秦玉明教授课题组，后申请直博，现为信息学院在读博士生，2023.1-2024.7到普瓦捷大学进行联合培养。曾参加国家自然科学基金面上项目吸引子经典理论及应用相关问题的研究、中央高校科研基金几类非线性发展方程解的整体存在性、渐近性及其精确能控性、国家留学基金联合培养博士研究生等项目。曾在 Proc. Roy. Soc. Edinburgh-A和Appl. Mathe. and Optim.发表论文，曾获内蒙古自治区优秀毕业生、东华大学恒逸奖学金、优秀学生干部等奖项。,

题目: Smooth conjugacy for random dynamical systems,

活动内容摘要: In this talk, we report recent results on various smooth conjugacy theorems for random dynamical systems based on their Lyapunov exponents.,

时间: 2023-06-18 08:30,

主讲人: 吕克宁,

主讲人简介: 吕克宁教授是微分方程与无穷维动力系统专家，曾任Brigham Young University和Michigan State University教授，现任四川大学教授，2017年获首届“张芷芬数学奖”，2020年入选AMS fellow，现任国际学术刊物JDE共同主编。他在不变流形和不变叶层，Sinai-Ruelle-Bowen测度，熵和Lyapunov指数以及随机动力系统的光滑共轭理论和随机偏微分方程的动力学方面做出了多个工作，相关论文发表在《Inventiones Mathematicae》、《Communications on Pure and Applied Mathematics》、《Memoirs of the American Mathematical Society》等学术期刊上。,

题目: Strong global and exponential attractors for a nonlinear strongly damped hyperbolic equation,

活动内容摘要: In this talk, we investigate the global well-posedness and the existence of strong global and exponential attractors for a nonlinear strongly damped hyperbolic equation in Ω⊂R^N:\nu_tt+Δ^2 u+Δ^2 u_t+Δϕ(Δu)=g(x),\n with the hinged boundary condition.  We show that  (i) when  the   nonlinearity ϕ is quasi-monotone and is of at most  the critical growth: 1≤p≤p^*:=(N+2)\/((N-2)^+ )(N≥2)  and g=0, the model has in phase space V_3×L^2 a trivial global and exponential attractor, respectively.  (ii) In particular when N=1, without any polynomial growth restriction for ϕ, the model has a strong global and a strong exponential attractor, respectively. These results deepen and extend the related research on this topic in recent literature. The method developed here allows us to establish the existence of the strong global and exponential attractor for this nonlinear model.\n,

时间: 2023-06-18 08:45,

主讲人: 杨志坚,

主讲人简介: 郑州大学理学博士，日本九州大学数理学博士，郑州大学2级教授，博士生导师，河南省跨世纪学术、技术带头人, 美国 《Mathematical Reviews》评论员，《Journal of Partial Differential Equations》期刊编委。主要研究非线性发展方程的整体适定性及对应的无穷维耗散动力系统的长时间动力学行为。主持完成4项国家自然科学基金面上项目。,

题目: Global smooth solutions to the 3D compressible viscous non-isentropic magnetohydrodynamic flows without magnetic diffusion,

活动内容摘要: How to construct the global smooth solutions to the compressible viscous, nonisentropic, non-resistive magnetohydrodynamic equations in T^3 appears to be unknown. In this talk, we give a positive answer to this problem. More precisely, we show a global stability result on perturbations near a strong background magnetic field to the 3D compressible viscous, non-isentropic, non-resistive magnetohydrodynamic equations. This stability result provides a significant example of the stabilizing effect of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit decay rate for the solutions to this nonlinear system.,

时间: 2023-06-18 09:30,

主讲人: 李用声,

主讲人简介: 李用声，华南理工大学数学学院教授，博士生导师。主要从事非线性发展程与无穷维动力系统的研究工作，涉及的方程有非线性色散方程和方程组（如Schrödinger方程及其方程组）、流体力学方程组等等，研究内容包括这些方程和方程组的解的存在性、唯一性、爆破性、衰减性、整体吸引子的存在性及其分形维数估计等。在国内外重要学术刊物上发表论文100余篇， SCI收录约80篇。先后主持5项国家自然科学基金项目，参加一项国家自然科学基金重点项目。曾被评为湖北省跨世纪学术骨干，作为主要完成人获得过国防科工委科技进步一等奖，曾获得全国优秀博士学位论文提名奖指导教师称号。,

题目: On the attractors of primitive equations of the large-scale atmosphere and ocean,

活动内容摘要: In this talk, we give some results on the attractors of primitive equations of the large-scale ocean. Firstly, we recall the global well-posedness and long-time dynamics for the viscous primitive equations describing the large-scale oceanic motion. Secondly, we introduce some results on the global attractors of primitive equations, such as the enhanced pullback attractors of 3D Primitive Equations.,

时间: 2023-06-18 10:30,

主讲人: 黄代文,

主讲人简介: 黄代文，男，2007年获中国工程物理研究院博士学位，现为北京应用物理与计算数学研究所研究员。主持完成了两项国家基金；作为主要参加人，完成了一项国家基金重点项目和一项面上项目。在Comm. Math. Phys., J. Func. Anal., J. Diff. Equ.等国际数学期刊上发表论文二十余篇。研究领域：非线性发展方程及其无穷维动力系统，主要研究大气、海洋科学和等离子体物理中的一些重要偏微分方程。,

题目: Well-posedness and data assimilation of the primitive equations coupled with multi-phase moisture atmosphere,

活动内容摘要: The occurrence and development of cloud and precipitation are the products of the combination of atmospheric dynamic, thermal processes and cloud microphysical processes. In order to understand the interaction between these influencing factors in more detail, we consider two moisture models with multi-phase for warm clouds, which consists of the primitive equations with full viscosity and only horizontal viscosity respectively, and a set of humidity equations where water is present in the form of water vapor, rainwater and cloud condensates. For the full viscosity case, we obtain the global existence of both quasi-strong solutions and strong solutions by introducing a new penalized function.  For the only horizontal viscosity case, we obtain the similar results by combining the idea of z-weak solution and the viscous elimination method. Some results concerned the uniqueness and data assimilation problems will also be mentioned. These works are joint with Shenyang Tan.,

时间: 2023-06-18 11:15,

主讲人: 刘文军,

主讲人简介: 刘文军，教授、博士生导师，中国工业与应用数学学会理事、江苏省高校“青蓝工程”中青年学术带头人及优秀团队负责人、江苏省“六大人才高峰”高层次人才。主要从事非线性偏微分方程及其在材料、生物、医学等领域交叉应用的研究。已主持国家自然科学基金项目5项，以及科技部国家外国专家项目、江苏省重点研发计划等项目。近5年在JFA, Phys. D, Appl. Math. Optim.等发表学术论文30余篇，获专利授权6项，主编出版教材3部。获得江苏省工业与应用数学青年奖、江苏省教育科学研究成果奖一等奖、江苏省教学成果一等奖等，所负责的“数学物理方程”课程入选国家级一流课程。多次指导学生获得大学生数学建模竞赛全国一等奖、美赛特等奖提名等奖项。,

题目: Longtime behavior of a diffuse interface model for two-phase magnetohydrodynamic flows in dimension two,

活动内容摘要: We introduce a diffuse interface model which describes the interaction between a magnetic field and two immiscible, conducting, incompressible fluids. The model consists of the Cahn-Hilliard equation for the order parameter coupled with the equations of resistive magnetohydrodynamics for the volume averaged velocity and for the magnetic field. The resulting evolution system is endowed with suitable initial and boundary conditions. Here we focus on its longtime behavior in dimension two. We show that we can define a dissipative dynamical system on a finite energy phase space and that system has the global attractor. Moreover, the backward uniqueness property holds on the global attractor. Convergence to equilibrium of a single trajectory will also be discussed.,

时间: 2023-06-18 14:00,

主讲人: Grasselli,

主讲人简介: Maurizio Grasselli 是意大利米兰理工大学的教授。他的研究领域是无穷维耗散动力系统。,

题目: Numerical attractors: existence, bounds, convergence and enlarged regularity,

活动内容摘要: In this talk, we focus on discretization of global attractors for p-Laplace or porous media lattice systems. More precisely, by the implicit Euler scheme, the continuous-time lattice systems are discretized as discrete-time systems. We then show the existence and bounds of numerical attractors as well as solutions for the discrete-time system with sufficiently small step sizes, and establish the upper semi-convergence of numerical attractors towards the global attractor as the step size tends to zero. We also study the numerical attractors and their approximations on the larger initial space.  The second-order Taylor expansion and discretization error on the enlarged space are established to prove the upper semi-continuity of the enlarged numerical attractors in step sizes, while an upper bound of the enlarged attractors is provided to establish the lower semi-continuity in special cases.,

时间: 2023-06-18 14:45,

主讲人: 李扬荣,

主讲人简介: 李扬荣，西南大学数学与统计学院，教授，博士生导师。博士毕业于南京大学（1996），博士后（北京应用物理与计算数学所）。现任重庆数学学会副理事长， 曾任中国数学会理事。主要研究随机偏微分方程及其随机吸引子，先后在J. Dyn. Diff. Equ，J. Diff. Equ，Physica D，J. Appl. Probab. ，Appl. Math. Opt. 等期刊上发表论文100余篇。,

题目: Data assimilation for dissipative system under environment noise,

活动内容摘要: In this talk, we first review the definition of data assimilation introduced by Titi. Then we use feedback control theory to study the data assimilation of dissipative system. Note that there will be random errors in the measurement and noise always exists in the real world, so we consider data assimilation of dissipative system with random errors under environment noise. We give a new mechanism for data assimilation problem.,

时间: 2023-06-18 15:30,

主讲人: 吕广迎,

主讲人简介: 吕广迎，男，1982年生，南京信息工程大学数学与统计学院，教授，博士生导师。研究兴趣：随机(偏)微分方程以及随机分析在金融、统计物理中的应用。现主持国家自然科学基金面上项目一项，主持完成国家基金3项，主持完成省部级项目6项。发表论文60余篇，部分结果发表在SIAM J. Math. Anal., J. Funct. Anal., J. Differential Equations等杂志上。2019年荣获河南省教育厅学术技术带头人称号。2022年入选江苏高校“青蓝工程”中青年学术带头人。,

题目: Robustness of exponentially κ-dissipative dynamical systems with perturbations,

活动内容摘要: We study the robustness of exponentially κ-dissipative dynamical systems with perturbations. For every perturbation parameter ε, we construct a compact set A_ε which is positive invariant and exponentially attracts bounded subsets. Moreover, we prove that for any η, there exists a δ>0 such that\ndist_X⁡(A_(ε_1 ),A_(ε_2 ) )⩽η\nprovided |ε_1-ε_2 |⩽δ.\n,

时间: 2023-06-18 16:30,

主讲人: 汪永海,

主讲人简介: 主要从事偏微分方程、无穷维动力系统专业领域的相关研究，主持并参与国家自然科学基金数学天元项目、国家自然科学基金青年基金项目、国家自然科学基金面上项目、国家自然科学基金重点项目、上海市自然科学基金项目、中央高校基本科研经费项目。在国外期刊上发表相关研究论文10余篇，如Nonlinear Analysis, Journal of Mathematical Analysis and Applications, Discrete and Continuous Dynamical Systems, Communications on Pure and Applied Analysis, Applied Mathematics and Computation, Asymptotic Analysis, Boundary Value Problems, Topological Methods in Nonlinear Analysis 等国际著名学术期刊。\n,

题目: Schrodinger方程的唯一延拓性不等式,

活动内容摘要: 在研究退化耗散Schrodinger方程的吸引子理论时，通常的能量估计和Gronwall不等式不足以证明有界吸收集的存在性。克服这一困难的重要工具是唯一延拓性不等式，即系统全体能量被局部区域能量控制。本报告将介绍我们关于薛定谔方程唯一延拓性不等式的两类结果：(1)两点时刻能观测不等式；(2)空间区域能观测集的刻画。,

时间: 2023-06-18 17:15,

主讲人: 王明,

主讲人简介: 王明，华中科技大学本科、博士，现任中国地质大学（武汉）数理学院副教授，硕士生导师。主要从事色散方程与无穷维动力系统方面的研究，主持国家自然科学基金面上项目、青年基金，担任Mathematical Reviews 评论员。目前在唯一延拓性不等式，耗散系统衰减性以及吸引子理论方面取得了一些进展。共发表论文30余篇，部分发表在J. Eur. Math. Soc. (JEMS)，Comm. Math. Phys.，J. Math. Pures Appl., SIAM J. Math. Anal.，JDE等期刊上。,