Related papers: A parabolic free boundary problem modeling electro…
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…
A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential…
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…
The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with…
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…
Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures with cross-sections of the order of microns ($\mu m$) and lengths of the order of tens or hundreds of microns. These structures are often plates or array of…
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…
We study a nonlinear wave equation appearing as a model for a membrane (without viscous effects) under the presence of an electrostatic potential with strength $\lambda$. The membrane has a unique stable branch of steady states…
Local well-posedness for a nonlinear parabolic-hyperbolic coupled system modelling Micro-Electro-Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has…
The parabolic problem $u_t-\Delta u=\frac{\lambda f(x)}{(1-u)^2}+P$ on a bounded domain $\Omega$ of $R^n$ with Dirichlet boundary condition models the microelectromechanical systems(MEMS) device with an external pressure term. In this…
The singular parabolic problem $u_t=\Delta u -\frac{\lambda f(x)}{(1+u)^2}$ on a bounded domain $\Omega$ of $R^N$ with Dirichlet boundary conditions, models the dynamic deflection of an elastic membrane in a simple electrostatic…
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…
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…
We report on low temperature measurements performed on micro-electro-mechanical systems (MEMS) driven deeply into the non-linear regime. The materials are kept in their elastic domain, while the observed non-linearity is purely of…
Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For…
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…
This paper is concerned with the nonlinear elliptic problem $-\Delta u=\frac{\lambda }{(a-u)^2}$ on a bounded domain $\Omega$ of $\mathbb{R}^N$ with Dirichlet boundary conditions. This problem arises from Micro-Electromechanical Systems…
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle…
We investigate the dynamics of membranes that are held by freely-rotating tethers in fluid flows. The tethered boundary condition allows periodic and chaotic oscillatory motions for certain parameter values. We characterize the oscillations…
We simulate the electrical response of multiple disjoint biological 3D cells undergoing an electropermeabilization process. Instead of solving the boundary value problem in the unbounded volume, we reduce it to a system of boundary…