2020年椭圆和抛物型偏微分方程进展研讨会

       地　　点： 新波谱楼12楼1217报告厅 

　　时　　间： 2020年1月7日（周二） 

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　　报告一 

　　报告题目：Ground state for Schr？dinger-Poisson-Slater system with unbounded potential 

　　报 告 人：王征平    教授    武汉理工大学 

　　时      间： 9：00--9：40 

　　Abstract 

　　In this talk, we give some recent results on the existence of ground state for nonlinear Schr？dinger-Poisson-Slater equation with unbounded potential. By using Ekeland’s variational principle we prove that there exists a ground state with negative energy level. For the special case of Schr？dinger-Poisson-Slater equation with harmonic potential, we show that the ground state must be nonradial.   

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　　报告二 

　　报告题目：Existence and blow-up of ground state solutions for some Kirchhoff equations 

　　报 告 人：  张贻民    教授    武汉理工大学 

　　时      间： 9：40--10：20 

　　Abstract 

　　For some  Kirchhoff functionals, we search for its $L^2$-normalized critical points.Firstly, we  give a complete classification with respect to the exponent $p$ for the existence of minimizers of these functionals, and  show that the minimizer of these functionals, if  exists,  is unique up to translations. Secondly, we search for the mountain pass type critical point for these functionals on  $L^2$ constraint manifold,  and also prove that this type critical  point  is unique up to translations. Moreover, we get some blow up properties  ground state solutions for this type Kirchhoff equations. 　  

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　　报告三 

　　报告题目：Ground states for some constraint variational problems 

　　报 告 人：曾小雨    副教授     武汉理工大学 

　　时    间：10：20--11：00 

　　Abstract 

　　For some constraint variational problems, which arise in Bose-Einstein condensation and Bose star models, we study the existence and uniqueness of minimizers. Moreover, by employing some technical energy estimates, we investigate the limit behavior of minimizers as parameters go to the thresholds. 　　  

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　　报告四 

　　报告题目：Convergence rate estimates for Alexandrov’s solution to the Monge-Ampere equation 

　　报 告 人：黄耿耿   副教授    复旦大学 

　　时    间：  11：00--11：40 

　　Abstract 

　　In this talk, we talk about error estimates for solutions to the Dirichlet problem of the Monge-Ampere equation det D² u=  in Ω, where f is a positive and continuous function and Ω is a bounded convex domain in the Euclidean space Rⁿ. We approximate the solution u by a sequence of convex polyhedra , which are generalised solutions to the Monge-Ampère equation in the sense of Aleksandrov, and the associated Monge- Ampère measures  are supported on a properly chosen grid in Ω. We will derive error estimates for the cases when  is smooth, H？lder continuous, and merely continuous. This is a joint work with Haodi Chen and Xu-Jia Wang. 　  

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　　报告五 

　　报告题目：ON THE VANISHING VISCOSITY LIMIT OF A CHEMOTAXIS MODEL 

　　报 告 人：陈化    教授    武汉大学 

　　时      间： 15：00--16：00 

　　Abstract 

　　A vanishing viscosity problem for the Patlak-Keller-Segel model is mentioned in this talk. This is a parabolic-parabolic system in a bounded domain , with a vanishing viscosity 0. We show that if the initial value lies in W^1,p  with p> max {2; n}, then there exists a unique solution  with its lifespan independent of . Furthermore, as  converges to the solution  of the limiting system in a suitable sense.   

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　　报告六 

　　报告题目：:一类p-Laplace方程特征值问题解的存在性与性态 

　　报 告 人：周焕松    教授    武汉理工大学 

　　时      间： 16：00--17：00 

　　Abstract 

　　本报告将主要介绍报告人及其合作者关于一类p-Laplace方程特征值问题的相关研究结果。报告内容主要包括应用约束变分方法建立解的存在性以及利用能量估计的思想分析解的渐近行为。 　  

　　欢迎参加！