一类刻画微机电模型四阶抛物型方程解的适定性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1718-1733.

一类刻画微机电模型四阶抛物型方程解的适定性

赖柏顺(),罗勍*()

^{湖南师范大学数学与统计学院长沙 410081}

收稿日期:2020-09-18 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 罗勍 E-mail:laibaishun@hunnu.edu.cn;10100095@vip.henu.edu.cn
作者简介:赖柏顺, E-mail: laibaishun@hunnu.edu.cn
基金资助:
国家自然科学基金(11971148)

Well-Posedness of a Fourth Order Parabolic Equation Modeling MEMS

Baishun Lai(),Qing Luo*()

^{School of Mathematics and Statistics, Hunan Normal University, Changsha 410081}

Received:2020-09-18 Online:2021-12-26 Published:2021-12-02
Contact: Qing Luo E-mail:laibaishun@hunnu.edu.cn;10100095@vip.henu.edu.cn
Supported by:
the NSFC(11971148)

摘要/Abstract

摘要：

该文考虑了有界区域上一类带奇异非线性项$（1-u）^{-2}$的四阶演化方程解的适定性.该模型具有很强的物理背景，它刻画了微机电模型的工作原理.首先，该文研究了四阶抛物方程解的适定性，该方程的适定性在文章[1]中通过半群理论得到验证，但是他们只限于区域空间维数为2维的情形.通过Faedo-Galerkin技巧，可以证明该方程在空间维数小于等于7的情形下解是适定的.

关键词: 微机电模型, 四阶演化方程, 适定性

Abstract:

In this paper, we consider a fourth order evolution equation involving a singular nonlinear term $\frac{\lambda}{(1-u)^{2}}$ in a bounded domain $\Omega \subset \mathbb{R}^{n}$. This equation arises in the modeling of microelectromechanical systems. We first investigate the well-posedness of a fourth order parabolic equation which has been studied in [1], where the authors, by the semigroup argument, obtained the well-posedness of this equation for $n\leq2$. Instead of semigroup method, we use the Faedo-Galerkin technique to construct a unique solution of the fourth order parabolic equation for $n\leq7$, which completes the result of [1].

Key words: Electrostatic MEMS, Fourth order evolution equation, Well-posedness

中图分类号:

O175

赖柏顺,罗勍. 一类刻画微机电模型四阶抛物型方程解的适定性[J]. 数学物理学报, 2021, 41(6): 1718-1733.

Baishun Lai,Qing Luo. Well-Posedness of a Fourth Order Parabolic Equation Modeling MEMS[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1718-1733.

参考文献

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