题目：Some Aspects in the Analysis of Asymptotic Behavior of Solutions to Some PDEs

报告人：Zheng-Chao Han   (Rutgers University)

摘要: In this expository talk aimed at graduate students and upper level undergraduates, I would like to use several examples to illustrate how to carry out the analysis of asymptotic behavior of solutions of some (geometric) PDEs. Such problems often arise when studying the behavior of a geometric object (such as a minimal surface or a harmonic map or a certain metric) near its singular points or the behavior of a solution of a certain evolution equation as times tends to infinity. A first step analysis is often to use rescaling to study the limiting behavior of a sequence of “blown-up” solutions. One often gets a limit as an “entire solution”. But the following issues need to be addressed:

(i) Can one classify the limits? Is it unique? If not, can one characterize them?

(ii) the convergence to any such a limit is often obtained after taking a subsequence and when restricted to any compact region of the domain, which does not directly give information about the limiting behavior of the original solution. Is it possible to prove the limiting behavior of the original solution using such information?

(iii) If the limits in (i) are not unique, how does one identify the appropriate limit in achieving (ii)?

(iv) Is it possible to prove a rate of convergence if one can carry out (i)—(iii)?

I will try to make the talk accessible to students with some familiarity to the behavior of harmonic functions in the Euclidean space and some exposure to undergraduate geometry

报告时间：2024年6月28日（周五）上午10:00-11:00

报告地点：教二楼927

联系人：戎小春、胥世成