关于 MEMS 建模中出现的准抛物线-超抛物线系统

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-05-11 DOI:10.1007/s10231-024-01465-9

Christoph Walker

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引用次数: 0

摘要

研究考虑了一个由准线性抛物方程和半线性双曲方程组成的耦合系统。该问题是微机电系统（MEMS）器件建模中的一个小长宽比极限问题，其中考虑到了器件的间隙宽度和气体压力。该系统被视为一种更普遍情况下的特例，其强解法的局部拟合性得到了证明。一般结果适用于不同的情况，包括抛物线方程与二阶或四阶半线性波方程的耦合，后者具有夹紧或钉牢边界条件。

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On a quasilinear parabolic–hyperbolic system arising in MEMS modeling

A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling of a MEMS device taking into account the gap width of the device and the gas pressure. The system is regarded as a special case of a more general setting for which local well-posedness of strong solutions is shown. The general result applies to different cases including a coupling of the parabolic equation to a semilinear wave equation of either second or fourth order, the latter featuring either clamped or pinned boundary conditions.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.