Southwest Jiaotong University School of Mathematics


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来源:   作者:黎定仕     日期:2018-12-04 18:16:39   点击数:  

题目: Recent progress on mean-square attractor, exponential attractor and critical parabolic equation

报告人:王业娟    教授、博士生导师    兰州大学

时间:20181209 日(星期日)0930-1020


摘要: The first result is used to establish the existence of a mean-square random attractor for stochastic parabolic partial differential equations, then we prove the existence of a compact positively invariant set which exponentially attracts any bounded set for abstract multi-valued semidynamical systems, and  apply the abstract theory to handle lattice dynamical systems and  reaction-diffusion equations with infinite delays. Finally, we formulate an abstract result allowing to treat the solutions of critical and super-critical equations as limits of solutionsto their regularizations. The abstract result is illustrated with the Navier-Stokes equation in space dimensions 2 to 4, and with the 2-D quasi-geostrophic equation. Various technical estimates related to that problems and their fractional generalizations are also presented.

个人简介:王业娟,兰州大学数学与统计学院教授、博士生导师,主要从事动力系统在生物动力学、控制系统、大气科学和金融中的应用;非线性分析;偏微分(分数阶)方程、随机微分方程的理论、应用与数值模拟。20056月在兰州大学获理学博士学位, 导师为钟承奎教授; 20057-20076月在上海大学理学院从事博士后研究工作,合作导师为周盛凡教授;20099-20109月在美国布朗大学应用数学系学术访问任Visiting Associate Professor,合作导师为John Mallet-Paret教授。在《J. Diff. Eqns.》、《SIAM J. NUMER. ANAL.》等国际著名杂志上已发表被SCI收录的学术论文30余篇。先后主持、完成国家自然科学基金,现正在主持两项国家自然科学基金面上项目,其中一项来自大气科学。