The first part of this article is an overview on some recent major developments in the field of analysis and partial different equations.It is a brief presentation given by the author at a round table discussion.The s...The first part of this article is an overview on some recent major developments in the field of analysis and partial different equations.It is a brief presentation given by the author at a round table discussion.The second part is a supplement of various details provided by several outstanding researchers on subjects.展开更多
In this paper, we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity. We prove that, asymptotically, the vortex-lines evolve according to the mean curvature flow with a forcing te...In this paper, we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity. We prove that, asymptotically, the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.展开更多
基金This article is initiated during a round table discussion at International Center for Mathematics in Southern University of Science and Technology(SUSTech)held in the January 2020.I am grateful to the wonderful organization and hospitality provided by Professors Tao Tang,Xiaoming Wang and Linlin Su.In the course of the preparation of this work,several colleagues have contributed to the scientific part of this review article.Here I would like to thank particularly:Chenjie Fan from University of Chicago,Jun Geng from Lanzhou University,Yanlin Liu from The Chinese Academy of Sciences,Xinan Ma from University of Sciences and Technology of China,Shuang Miao and Kelei Wang from Wuhan UniversityPing Zhang from The Chinese Academy of Sciences and Zhifei Zhang from Beijing University.Their enthusiasm and passion have greatly improved the presentation and the quality of this work.
文摘The first part of this article is an overview on some recent major developments in the field of analysis and partial different equations.It is a brief presentation given by the author at a round table discussion.The second part is a supplement of various details provided by several outstanding researchers on subjects.
基金This work is partially supported by the National Natural Science Foundation of China (Grant Nos.10071067,10471119)the Excellent Yong Teachers Program of the Ministry of Education of China.
文摘In this paper, we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity. We prove that, asymptotically, the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.
