Hyperbolic quenching problem with damping in the micro-electro mechanical system device

Jong-Shenq Guo; Bo-Chih Huang

doi:10.3934/dcdsb.2014.19.419

Article Contents

2014, Volume 19, Issue 2: 419-434. Doi: 10.3934/dcdsb.2014.19.419

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Hyperbolic quenching problem with damping in the micro-electro mechanical system device

Jong-Shenq Guo^1, and
Bo-Chih Huang^2,

1.
Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137
2.
Department of Mathematics, Tamkang University, Tamsui, New Taipei City 25137

Received: April 30, 2013

Revised: July 31, 2013

Published: February 2014

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Abstract

We study the initial boundary value problem for the damped hyperbolic equation arising in the micro-electro mechanical system device with local or nonlocal singular nonlinearity. For both cases, we provide some criteria for quenching and global existence of the solution. We also derive the existence of the quenching curve for the corresponding Cauchy problem with local source.

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Mathematics Subject Classification: Primary: 35L71, 35L81; Secondary: 35A01, 35L20, 74H35, 74K15.

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References

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