Wellposedness of an elliptic-dispersive coupled system for MEMS

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-04-27 DOI:10.3934/dcds.2023055

H. Gimperlein, Runan He, A. Lacey

引用次数: 1

Abstract

In this work, we study the local wellposedness of the solution to a nonlinear elliptic-dispersive coupled system which serves as a model for a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device consists of two parallel plates separated by a gas-filled thin gap. The nonlinear elliptic-dispersive coupled system modelling the device combines a linear elliptic equation for the gas pressure with a semilinear dispersive equation for the gap width. We show the local-in-time existence of strict solutions for the system, by combining elliptic regularity results for the elliptic equation, Lipschitz continuous dependence of its solution on that of the dispersive equation, and then local-in-time existence for a resulting abstract dispersive problem. Semigroup approaches are key to solve the abstract dispersive problem.

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MEMS椭圆色散耦合系统的适位性

在这项工作中，我们研究了作为微机电系统(MEMS)模型的非线性椭圆-色散耦合系统解的局部适定性。一个简单的静电驱动MEMS电容器装置由两个平行的板由一个充满气体的薄间隙分开。该装置的非线性椭圆-色散耦合系统将气体压力的线性椭圆方程与间隙宽度的半线性色散方程相结合。通过结合椭圆方程的椭圆正则性结果、其解与色散方程解的Lipschitz连续依赖以及由此得到的一个抽象色散问题的局部存在性，证明了该系统严格解的局部存在性。半群方法是解决抽象色散问题的关键。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.