Some Results Related to MEMS-Type Equations

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.