Some Results Related to MEMS-Type Equations

发布者:文明办发布时间:2024-06-17浏览次数:75


主讲人:张艳艳 华东师范大学副教授


时间:2024年6月18日15:00


地点:三号楼332室


举办单位:数理学院


主讲人介绍:张艳艳,现任华东师范大学数学科学学院副教授。2005年在河南大学取得理学学士学位,2010年在复旦大学获得博士学位,后在华东师范大学任职至今。主要研究领域是偏微分方程的理论研究及其应用。曾荣获2012年华东师范大学第九届青年教师教学比赛二等奖。


内容介绍:We will discuss some results related to several classes of semilinear elliptic equations and evolution equations derived from fields such as Micro-Electro-Mechanical Systems (MEMS). In the first part of this talk, we will examine the behaviors of rupture solutions for a class of elliptic MEMS equations in . We will first analyze the classification of all possible singularities at the rupture point for rupture solutions . In particular, we show that sometimes admits only the isotropic singularity at , and otherwise may admit an anisotropic singularity at . Secondly, global solutions in (their existence and their behavior near as well as near ) are also studied. In the second part, we will discuss the asymptotic behaviors of global solutions of two types of MEMS equations (nonlocal second-order MEMS equations and fourth-order MEMS equations with Dirichlet boundary conditions), for which the comparison principle is not available. This is a joint work with Y.J. Guo, F. Zhou, Qing Li, Yufei Wei, and Wenlong Wu.