In this text, we presented the Nachaoui's iterative alternating method for solving the Cauchy
problem governed by the convection-diffusion equation. The method is an iterative algorithm …

Abstract The Nernst-Planck-Poisson (NPP) system of equations is used to study the ion
diffusion mechanism in materials, commonly used in storage batteries and solid oxide fuel …

In this article, we study the existence of weak solutions to a nonlinear Dirichlet boundary
value problem with a Kirchhoff term. The Berkovits topological degree is applied to an …

A problem of determining the characteristics of a semiconductor can be reduced to the study
of the quasi-variational inequality,(J. Abouchabaka, R. Aboulaïch, A. Nachaoui and A …

The drift-diffusion model can be described by a nonlinear Poisson equation for the
electrostatic potential coupled with a system of convection-reaction-diffusion equations for …

In this paper, we discuss an inverse problem of determining a part of the boundary of the
depletion region of semiconductor devices. The existence of the unique solution is proved …

Electrical potentials in a junction field transistor can be calculated using a simplified model
based on a complete depletion assumption. This gives rise to a free boundary problem. We …

In this paper, we develop an adaptive finite element method for the nonlinear steady-state
Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities …

In this paper we generalize the abstract results of Mock and Marcowich [13, 12] for
convergence of discrete Van Roosbroeck systems [12, 13, 17], to the case when the …

This paper is concerned with the analysis of global uniqueness of the solution to the drift—
diffusion models, for stationary flow of charges carriers in semiconductor devices. Two …