Related papers: A parabolic free boundary problem modeling electro…
Micro-Electro Mechanical Systems (MEMS) are defined as very small structures that combine electrical and mechanical components on a common substrate. Here, the electrostatic-elastic case is considered, where an elastic membrane is allowed…
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. The authors have justified the well-posedness of this problem and have…
A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This…
Elastic membranes composed of paramagnetic beads offer the possibility of assembling versatile actuators operated autonomously by external magnetic fields. Here we develop a theoretical framework to study shapes of such paramagnetic…
In this paper, a coherent boundary value problem to model metamaterials' behavior based on the relaxed micromorphic model is established. This boundary value problem includes well-posed boundary conditions, thus disclosing the possibility…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
A continuum electromechanical model is proposed to describe the membrane curvature induced by electrostatic interactions in a solvated protein-membrane system. The model couples the macroscopic strain energy of membrane and the…
We present the stability analysis of two free boundary problems arising in biofilm modelling. The first, introduced in the 1980s by Wanner and Gujer, is related to the competition between autotrophic and heterotrophic bacteria in a biofilm…
This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…
Recently, we have proposed a new free boundary problem representing the bread baking process in a hot oven. Unknown functions in this problem are the position of the evaporation front, the temperature field and the water content. For…
A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling of a MEMS device taking into account the gap width of the…
We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle…
This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micro-Electro-Mechanical Systems (MEMS) and are depending on a…
Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures (plates or array of thin beams) with cross-sections of the order of microns and lengths of the order of tens or hundreds of microns. Electrostatic forces play…
In this paper, we study a free boundary problem for a class of parabolic-elliptic type chemotaxis model in high dimensional symmetry domain \Omega. By using the contraction mapping principle and operator semigroup approach, we establish the…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. In previous papers, we have established well-posedness of this problem and…
This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize…
In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix-degrading enzymes, which satisfy a coupled system of PDEs with a free boundary. For this coupled parabolic-hyperbolic…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…