On a general family of nonautonomous elliptic and parabolic equations

Dong Ye; Feng Zhou

doi:10.1007/s00526-009-0262-1

On a general family of nonautonomous elliptic and parabolic equations

Dong Ye^*
, Feng Zhou

^*此作品的通讯作者

数学科学学院

Université de Lorraine

科研成果: 期刊稿件 › 文章 › 同行评审

30 引用（Scopus）

摘要

We consider the parabolic equation u_t - Δu = λf (x)g(u) as well as the corresponding elliptic problem, with a nonnegative profile f and a positive nondecreasing convex function g verifying lim_{u→ 1}-g(u) = ∞. Our study is motivated by a simplified Micro-Electromechanical Systems (MEMS) device model. We extend or improve many qualitative and quantitative results for the MEMS modeling to this very general setting, which help us to understand more about the influence of f on the pull-in voltage λ* and the quenching phenomenon. Especially, we show some new estimates for λ* and the quenching time T.

源语言	英语
页（从-至）	259-274
页数	16
期刊	Calculus of Variations and Partial Differential Equations
卷	37
期	1
DOI	https://doi.org/10.1007/s00526-009-0262-1
出版状态	已出版 - 11月 2009

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AB - We consider the parabolic equation ut - Δu = λf (x)g(u) as well as the corresponding elliptic problem, with a nonnegative profile f and a positive nondecreasing convex function g verifying limu→ 1-g(u) = ∞. Our study is motivated by a simplified Micro-Electromechanical Systems (MEMS) device model. We extend or improve many qualitative and quantitative results for the MEMS modeling to this very general setting, which help us to understand more about the influence of f on the pull-in voltage λ* and the quenching phenomenon. Especially, we show some new estimates for λ* and the quenching time T.

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On a general family of nonautonomous elliptic and parabolic equations

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