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

Guo, Jong‐Shenq; Huang, Bo-Chih

doi:10.3934/dcdsb.2014.19.419

Cited by 13 publications

(11 citation statements)

References 20 publications

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“…Also in the hyperbolic problem, we have similar results to those in the parabolic case, i.e., the global existence [3,26,38], the quenching [3,26,32,38], the estimate of the quenching time [32] and the singularity of the derivative [2]. In the damped hyperbolic case, we have the global existence [27] and quenching [15,27]. Next recently the nonlocal problem…”

Section: Introductionsupporting

confidence: 53%

“…Although we can not apply the comparison principle owing to the nonlocal term, in the elliptic and parabolic problem, there are similar results to those without nonlocal term, i.e., the global existence [14,16,20], its asymptotic behaviour [20], the quenching [14,16,20] and its stationary solution [14,16,20,22,33,36]. For a hyperbolic and damped hyperbolic operator A, we have the results of the global existence [15,22] and the quenching [22] for Ω = (0, 1). If we assume that the domain and the solution are radially symmetric,…”

Section: Introductionmentioning

confidence: 57%

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Global existence and quenching for a damped hyperbolic MEMS equation with the fringing field

Miyasita¹

2017

Tamkang J. Math.

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Abstract. We study a damped hyperbolic MEMS equation with the fringing field. It arises in the Micro-Electro Mechanical System(MEMS) devices. We give some criteria for global existence and quenching of the solution. First we establish a time-local solution by a contraction mapping theorem. This procedure is standard. Next we show that there exists a global solution for the small parameter and initial value. Finally, we deal with the quenching result for the large parameter.

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Section: Introductionsupporting

confidence: 53%

Section: Introductionmentioning

confidence: 57%

Global existence and quenching for a damped hyperbolic MEMS equation with the fringing field

Miyasita¹

2017

Tamkang J. Math.

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“…With the increase of the displacement pressure gradient, the shear force of the wall fluid becomes larger and the proportion of movable fluid grows, indicating a thinner boundary layer [22] (See Figure 4). From Equations (8), (10) and (11), the expression of boundary layer thickness can be obtained. 4…”

Section: Representation Of Boundary Layer Thicknessmentioning

confidence: 99%

“…And the deviation declines in the form of exponential function with the increase of ∇ P (See Figure 3). So as to reflect the From Equations (8), (10) and (11), the expression of boundary layer thickness can be obtained.…”

Section: Representation Of Boundary Layer Thicknessmentioning

confidence: 99%

“…Therefore, figuring out microscopic flow law in consideration of micro scale effect is of great importance to the development of tight oil reservoirs. The research of micro-machining technology and micro-electro-mechanical system triggers a new field for the study of micro scale flow, which provides a new insight for studying fluid flow in tight reservoirs [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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A Study to Investigate Fluid-Solid Interaction Effects on Fluid Flow in Micro Scales

et al. 2018

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Due to micro-nanopores in tight formation, fluid-solid interaction effects on fluid flow in porous media cannot be ignored. In this paper, a novel model which can characterize micro-fluid flow in micro scales is proposed. This novel model has a more definite physical meaning compared with other empirical models. And it is validated by micro tube experiments. In addition, the application range of the model is rigorously analyzed from a mathematical view, which indicates a wider application scope. Based on the novel model, the velocity profile, the average flow velocity and flow resistance in consideration of fluid-solid interaction are obtained. Furthermore, the novel model is incorporated into a representative pore scale network model to study fluid-solid interactions on fluid flow in porous media. Results show that due to fluid-solid interaction in micro scales, the change rules of the velocity profile, the average flow velocity and flow resistance generate obvious deviations from traditional Hagen-Poiseuille’s law. The smaller the radius and the lower the displacement pressure gradient (∇P), the more obvious the deviations will be. Moreover, the apparent permeability in consideration of fluid-solid interaction is no longer a constant, it increases with the increase of ∇P and non-linear flow appears at low ∇P. This study lays a good foundation for studying fluid flow in tight formation.

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Existence and uniqueness for a coupled parabolic‐hyperbolic model of MEMS

Gimperlein,

He,

Lacey

2024

Math Methods in App Sciences

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Local wellposedness for a nonlinear parabolic‐hyperbolic coupled system modeling Micro‐Electro‐Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has motion modeled by a semilinear hyperbolic equation. The gap between the plates contains a gas and the gas pressure is taken to obey a quasilinear parabolic Reynolds' equation. Local‐in‐time existence of strict solutions of the system is shown, using well‐known local‐in‐time existence results for the hyperbolic equation, then Hölder continuous dependence of its solution on that of the parabolic equation, and finally getting local‐in‐time existence for a combined abstract parabolic problem. Semigroup approaches are vital for the local–in‐time existence results.

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

Cited by 13 publications

References 20 publications

Global existence and quenching for a damped hyperbolic MEMS equation with the fringing field

Global existence and quenching for a damped hyperbolic MEMS equation with the fringing field

A Study to Investigate Fluid-Solid Interaction Effects on Fluid Flow in Micro Scales

Existence and uniqueness for a coupled parabolic‐hyperbolic model of MEMS

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