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The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system (MEMS) is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a…

Analysis of PDEs · Mathematics 2012-11-27 Joachim Escher , Philippe Laurencot , Christoph Walker

The dynamics of a free boundary problem for electrostatically actuated microelectromechanical systems (MEMS) is investigated. The model couples the electric potential to the deformation of the membrane, the deflection of the membrane being…

Analysis of PDEs · Mathematics 2013-02-26 Joachim Escher , Philippe Laurencot , Christoph Walker

A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid…

Analysis of PDEs · Mathematics 2014-09-10 Philippe Laurencot , Christoph Walker

A moving boundary problem with two free boundaries modeling a two-dimensional idealized MEMS device with pull-in instability is discussed. We use a fixed point argument to show that the model possesses stationary solutions for small source…

Analysis of PDEs · Mathematics 2014-07-15 Martin Kohlmann

Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically…

Analysis of PDEs · Mathematics 2014-09-26 Philippe Laurencot , Christoph Walker

A stationary free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at…

Analysis of PDEs · Mathematics 2021-03-12 Katerina Nik

We discuss an evolution free boundary problem of mixed type with two free boundaries modeling an idealized electrostatically actuated MEMS device. While the electric potential is the solution of an elliptic equation, the dynamics of the…

Analysis of PDEs · Mathematics 2015-08-11 Martin Kohlmann

The dynamical and stationary behaviors of a fourth-order evolution equation with clamped boundary conditions and a singular nonlocal reaction term, which is coupled to an elliptic free boundary problem on a non-smooth domain, are…

Analysis of PDEs · Mathematics 2013-08-29 Philippe Laurencot , Christoph Walker

We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potential in the three-dimensional time-varying region between the…

Analysis of PDEs · Mathematics 2015-06-02 Philippe Laurencot , Christoph Walker

A parabolic free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at…

Analysis of PDEs · Mathematics 2021-03-12 Katerina Nik

In this paper, we reformulate a mathematical model for the dynamics of an idealized electrostatically actuated MEMS device with two elastic membranes as an initial value problem for an abstract quasilinear evolution equation. Applying the…

Analysis of PDEs · Mathematics 2015-08-11 Martin Kohlmann

A two-dimensional free boundary transmission problem arising in the modeling of an electrostatically actuated plate is considered and a representation formula for the derivative of the associated electrostatic energy with respect to the…

Analysis of PDEs · Mathematics 2022-02-22 Philippe Laurençot , Christoph Walker

We consider a parabolic problem with Robin boundary condition which arises when the edge of a micro-electro-mechanical-system (MEMS) device is connected with a flexible nonideal support. Then via a rigorous analysis we investigate the…

Analysis of PDEs · Mathematics 2020-07-09 Jong-Shenq Guo , N. I. Kavallaris , Chi-Jen Wang , Cherng-Yih Yu

We analyze the nonlinear elliptic problem $\Delta u=\frac{\lambda f(x)}{(1+u)^2}$ on a bounded domain $\Omega$ of $\R^N$ with Dirichlet boundary conditions. This equation models a simple electrostatic Micro-Electromechanical System (MEMS)…

Analysis of PDEs · Mathematics 2007-05-23 Nassif Ghoussoub , Yujin Guo

The occurrence of a finite time singularity is shown for a free boundary problem modeling microelectromechanical systems (MEMS) when the applied voltage exceeds some value. The model involves a singular nonlocal reaction term and a…

Analysis of PDEs · Mathematics 2014-02-03 Joachim Escher , Philippe Laurencot , Christoph Walker

A free boundary problem modeling a microelectromechanical system (MEMS) consisting of a fixed ground plate and a deformable top plate is considered, the plates being held at different electrostatic potentials. It couples a second order…

Analysis of PDEs · Mathematics 2016-12-20 Philippe Laurençot , Christoph Walker

The objective of our paper is to investigate fractional elliptic equations of the form $(-\Delta)^s u=\frac{\lambda }{(a-u)^2}$ within a bounded domain $\Omega$, subject to zero Dirichlet boundary conditions. Here, $s\in(0,1)$, $\lambda>0$,…

Analysis of PDEs · Mathematics 2026-02-17 Huyuan Chen , Jialei Jiang , Jun Wang

An idealized electrostatically actuated microelectromechanical system (MEMS) involving an elastic plate with a heterogeneous dielectric material is considered. Starting from the electrostatic and mechanical energies, the governing evolution…

Analysis of PDEs · Mathematics 2017-07-06 Philippe Laurencot , Christoph Walker

We consider two models, a free boundary problem and a simplification thereof, which describe a soap film bridge subjected to an electrostatic force. For both models, we construct stationary solutions if the force is small, analyse their…

Analysis of PDEs · Mathematics 2024-09-30 Lina Sophie Schmitz

In this work we numerically compute the bifurcation curve of stationary solutions for the free boundary problem for MEMS in one space dimension. It has a single turning point, as in the case of the small aspect ratio limit. We also find a…

Analysis of PDEs · Mathematics 2015-07-07 Gilberto Flores , Noel F. Smyth
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