相关论文: On an elliptic-parabolic MEMS model with two free …
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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, $s\in(0,1)$, $\lambda>0$,…
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…
We consider a two-phase elliptic-parabolic moving boundary problem modelling an evaporation front in a porous medium. Our main result is a proof of short-time existence and uniqueness of strong solutions to the corresponding nonlinear…
We study the local well-posedness of the solution to a coupled nonlinear elliptic-parabolic system which models electrical discharge in a Micro-Electro-Mechanical System (MEMS). A simple MEMS capacitor device contains two plates acting as…
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)…
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…
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…
We study the two-phase Muskat--Verigin free-boundary problem for elliptic equations with nonlinear sources. The existence of a smooth solution and a smooth free boundary is proved locally in time by applying the parabolic regularization of…
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to…
In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device has two…