Related papers: A stationary free boundary problem modeling electr…

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…

In this paper, we study a free boundary problem for a class of nonlinear nonautonomous size structured population model. Using the comparison principle and upper lower solution methods, we establish the existence of the solution for such…

If a differential equation in a Banach manifold is invariant or quasi-invariant under the action of one or more Lie groups, then its stationary points cannot be isolated, so that classical linearized stability theorem does not apply to it.…

A new homogenization-free boundary condition is introduced for the design of metasurfaces. The boundary condition, linking the tangential electric field to the induced surface current density within a unit cell, is described as a matrix…

We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape…

We study a fractional analogue of a plasma problem arising from physics. Specifically, for a fixed bounded domain $\Omega$ we study solutions to the eigenfunction equation \[ (- \Delta)^s u = \lambda(u- \gamma)_+ \] with $u \equiv 0$ on…

Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature…

We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…

We perform a variational analysis of an elastic membrane spanning a closed curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic membranes proving the existence of equilibria and finding…

We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type…

The current state of the art for analytical and computational modelling of deformation in nonlinear electroelastic and magnetoelastic membranes is reviewed. A general framework and a list of methods to model large deformation and associated…

So far most studies on mathematical models for microelectromechanical systems (MEMS) are focused on the so-called small aspect ratio model which is a wave or beam equation with a singular source term. It is formally derived by setting the…

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…

This paper is concerned with the elliptic equation $-\Delta u=\frac{\lambda }{(a-u)^p}$ in a connected, bounded $C^2$ domain $\Omega$ of $\mathbb{R}^N$ subject to zero Dirichlet boundary conditions, where $\lambda>0$, $N\geq 1$, $p>0$ and…

We extend the results obtained in \cite{Dov22} by introducing a new class of boundary value problems involving non-local dynamic boundary conditions. We focus on the problem to find a solution to a local problem on a domain $\Omega$ with…

We show that the open-loop transfer functions and the stability margins may be defined within the recent model-free control setting. Several convincing computer experiments are presented including one which studies the robustness with…

For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale approximations. There are no assumptions of periodicity involved…

For the system of cold plasma equations describing the motion of electrons in the field of stationary ions, we consider the Riemann problem posed at an impenetrable interface between two media. These media differ in the magnitude of the…

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…

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…