MEMS椭圆色散耦合系统的适位性

IF 1.1 3区数学 Q1 MATHEMATICS

Discrete and Continuous Dynamical Systems Pub Date : 2023-04-27 DOI:10.3934/dcds.2023055

H. Gimperlein, Runan He, A. Lacey

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引用次数: 1

摘要

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。

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Wellposedness of an elliptic-dispersive coupled system for MEMS

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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来源期刊

Discrete and Continuous Dynamical Systems 数学-数学

CiteScore

2.50

自引率

0.00%

发文量

175

审稿时长

6 months

期刊介绍： DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.