湘潭大学“分数微分方程理论及其应用”研究团队

来源:日期:2019-01-11

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团队负责人周勇教授

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团队主要成员

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获奖证书和专著

分数阶微积分始于三百多年前。近十年来,分数阶微积分在许多学科领域发挥了非常重要的作用,已被公认为描述长记忆过程的最好工具之一。分数阶模型不仅使工程师和物理学家感兴趣,而且对于数学家来说也是有趣的。在这些模型中,包含分数导数的偏微分方程所描述的模型是非常重要的,它们的性质比经典的整数阶方程更为复杂,其理论研究是一项非常艰巨的任务。湘潭大学“分数微分方程理论及其应用”研究团队致力于分数微分方程的基本理论、分数阶建模和数值方法的研究,并将分数阶微积分应用于科学和工程中的一些重要问题。该团队由周勇教授负责,主要成员有李成福教授、兰永红教授、张璐博士、彭丽博士、何家维、王静娜等。

近年来,该团队与20余个国家和地区的研究人员有着广泛的学术合作;团队承担了国家自然科学基金项目7项、教育部博士点基金项目2项、湖南省自然科学基金重点项目等科研项目;主要研究领域包括分数哈密顿系统同宿轨的存在性,时间分数Navier-Stokes方程、Schrödinger方程和扩散方程的适定性和正则性,分数非线性系统的最优控制。特别是他们解决了分数发展方程适定性理论中最核心和关键的问题。

团队负责人周勇教授是多个国际数学杂志的编委和客座编委,已出版学术专著(英文)6部;在Mathematische AnnalenJournal of Functional AnalysisBulletin des Sciences MathématiqueComptes Rendus MathématiqueNonlinear Dynamics等重要学术期刊上发表论文200余篇,其中26篇论文被列入ESI 高被引论文(Highly Cited Papers);获得教育部自然科学二等奖和湖南省自然科学二等奖。周勇教授于2014年获得汤森路透(Thomson Reuters)高被引科学家奖, 20142017年连续四年入选爱思唯尔(Elsevier)中国高被引学者。

Research Team for “Theory and Applications of Fractional Differential Equations”of Xiangtan University

The fractional calculus started more than three centuries ago. In the last decade, fractional calculus has been playing a very important role in various scientific fields. In fact, it has been recognized as one of the best tools to describe long-memory processes. Fractional-order models are interesting not only for engineers and physicists, but also for mathematicians. The most important among such models are those described by partial differential equations containing fractional derivatives. Their evolutions behave in a much more complex way than in the classical integer-order case and the study of the corresponding theory is a hugely demanding task. The research team for “Theory and Applications of Fractional Differential Equations” is devoted to studying the basic theory for fractional differential equations, fractional order modeling and numerical methods, and applying fractional calculus to some important problems in science and engineering. This team is mainly composed of Professors Yong Zhou, Chengfu Li, Yonghong Lan, and Dr. Lu Zhang, Li Peng, Jiawei He, Jingna Wang.

In the past years, the team carried out extensive academic exchanges and scientific cooperations with more than 20 overseas researchers including those in the United States, France, Australia, Spain, Italy, Slovakia, Belgium, Portugal, Turkey, India, Iran, Saudi Arabia and so on. In recent years, the group has undertaken more than 10 projects including National Natural Science Foundation, Specialized Research Fund for the Doctoral Program of Higher Education and Key Projects of Hunan Provincial Natural Science Foundation. The research team focused on studying the existence of homoclinic orbits for fractional Hamiltonian systems, well -posedness and regularity of the time fractional Navier-Stokes equations, Schrödinger equations and diffusion equations, and optimal control of fractional nonlinear systems. In particular, they solved the most important and key problems in the well posedness theory of fractional evolution equations.

The team leader Professor Yong Zhou serves on the editorial boards of several international mathematical journals. He has published 6 monographs and more than 200 papers in the journals such as Mathematische Annalen, Journal of Functional Analysis, Bulletin des Sciences Mathématiques, Comptes Rendus Mathématique and Nonlinear Dynamics, over 26 papers of which were included in ESI Highly Cited Papers. He was awarded the second prize of Natural Science of Ministry of Education and the second prize of Natural Science of Hunan province. Professor Yong Zhou won Highly Cited Researcher Award from Thomson Reuters in 2014, and was included in the list of Most Cited Chinese Researchers by Elsevier from 2014 to 2017.

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