Some Results Related to MEMS-Type Equations

主講人：張艷艷 華東師范大學副教授

時間：2024年6月18日15：00

地點：三號樓332室

舉辦單位：數(shù)理學院

主講人介紹：張艷艷，現(xiàn)任華東師范大學數(shù)學科學學院副教授。2005年在河南大學取得理學學士學位，2010年在復旦大學獲得博士學位，后在華東師范大學任職至今。主要研究領(lǐng)域是偏微分方程的理論研究及其應(yīng)用。曾榮獲2012年華東師范大學第九屆青年教師教學比賽二等獎。

內(nèi)容介紹：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.