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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

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

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

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

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

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 a free boundary problem modeling electrostatic microelectromechanical systems. The model consists of a fourth-order damped wave equation for the elastic plate displacement which is coupled to an elliptic equation for the…

Analysis of PDEs · Mathematics 2014-04-28 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

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

A free boundary problem describing small deformations in a membrane based model of electrostatically actuated MEMS is investigated. The existence of stationary solutions is established for small voltage values. A justification of the widely…

Analysis of PDEs · Mathematics 2013-01-28 Philippe Laurencot , Christoph Walker

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

An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…

Analysis of PDEs · Mathematics 2017-04-20 G. Buttazzo , G. Cardone , S. A. Nazarov

We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…

Fluid Dynamics · Physics 2025-05-20 Philippe H. Trinh , Stephen K. Wilson , Howard A. Stone

The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems (MEMS)…

Analysis of PDEs · Mathematics 2017-05-17 Philippe Laurencot , Christoph Walker

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

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

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

We address a free boundary model for the compressible Euler equations where the free boundary, which is elastic, evolves according to a weakly damped fourth order hyperbolic equation forced by the fluid pressure. This system captures the…

Analysis of PDEs · Mathematics 2023-11-16 Igor Kukavica , Šárka Nečasová , Amjad Tuffaha

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

The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values…

Analysis of PDEs · Mathematics 2009-12-22 Helmut Abels , Maria Giovanna Mora , Stefan Müller
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