團(tuán)隊(duì)負(fù)責(zé)人周勇教授
團(tuán)隊(duì)主要成員
獲獎(jiǎng)證書(shū)和專(zhuān)著
分?jǐn)?shù)階微積分始于三百多年前。近十年來(lái)，分?jǐn)?shù)階微積分在許多學(xué)科領(lǐng)域發(fā)揮了非常重要的作用，已被公認(rèn)為描述長(zhǎng)記憶過(guò)程的最好工具之一。分?jǐn)?shù)階模型不僅使工程師和物理學(xué)家感興趣，而且對(duì)于數(shù)學(xué)家來(lái)說(shuō)也是有趣的。在這些模型中，包含分?jǐn)?shù)導(dǎo)數(shù)的偏微分方程所描述的模型是非常重要的，它們的性質(zhì)比經(jīng)典的整數(shù)階方程更為復(fù)雜，其理論研究是一項(xiàng)非常艱巨的任務(wù)。湘潭大學(xué)“分?jǐn)?shù)微分方程理論及其應(yīng)用”研究團(tuán)隊(duì)致力于分?jǐn)?shù)微分方程的基本理論、分?jǐn)?shù)階建模和數(shù)值方法的研究，并將分?jǐn)?shù)階微積分應(yīng)用于科學(xué)和工程中的一些重要問(wèn)題。該團(tuán)隊(duì)由周勇教授負(fù)責(zé)，主要成員有李成福教授、蘭永紅教授、張璐博士、彭麗博士、何家維、王靜娜等。
近年來(lái)，該團(tuán)隊(duì)與20余個(gè)國(guó)家和地區(qū)的研究人員有著廣泛的學(xué)術(shù)合作；團(tuán)隊(duì)承擔(dān)了國(guó)家自然科學(xué)基金項(xiàng)目7項(xiàng)、教育部博士點(diǎn)基金項(xiàng)目2項(xiàng)、湖南省自然科學(xué)基金重點(diǎn)項(xiàng)目等科研項(xiàng)目；主要研究領(lǐng)域包括分?jǐn)?shù)哈密頓系統(tǒng)同宿軌的存在性，時(shí)間分?jǐn)?shù)Navier-Stokes方程、Schr?dinger方程和擴(kuò)散方程的適定性和正則性，分?jǐn)?shù)非線(xiàn)性系統(tǒng)的最優(yōu)控制。特別是他們解決了分?jǐn)?shù)發(fā)展方程適定性理論中最核心和關(guān)鍵的問(wèn)題。
團(tuán)隊(duì)負(fù)責(zé)人周勇教授是多個(gè)國(guó)際數(shù)學(xué)雜志的編委和客座編委，已出版學(xué)術(shù)專(zhuān)著（英文）6部；在Mathematische Annalen，Journal of Functional Analysis，Bulletin des Sciences Mathématique，Comptes Rendus Mathématique，Nonlinear Dynamics等重要學(xué)術(shù)期刊上發(fā)表論文200余篇，其中26篇論文被列入ESI 高被引論文（Highly Cited Papers）；獲得教育部自然科學(xué)二等獎(jiǎng)和湖南省自然科學(xué)二等獎(jiǎng)。周勇教授于2014年獲得湯森路透（Thomson Reuters）高被引科學(xué)家獎(jiǎng)， 2014－2017年連續(xù)四年入選愛(ài)思唯爾（Elsevier）中國(guó)高被引學(xué)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, Schr?dinger 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.
