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Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations

Yue-Jun Peng — 2001

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We deal with boundary layers and quasi-neutral limits in the drift-diffusion equations. We first show that this limit is unique and determined by a system of two decoupled equations with given initial and boundary conditions. Then we establish the boundary layer equations and prove the existence and uniqueness of solutions with exponential decay. This yields a globally strong convergence (with respect to the domain) of the sequence of solutions and an optimal convergence rate O ( ε 1 2 ) to the quasi-neutral...

Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations

Yue-Jun Peng — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We deal with boundary layers and quasi-neutral limits in the drift-diffusion equations. We first show that this limit is unique and determined by a system of two decoupled equations with given initial and boundary conditions. Then we establish the boundary layer equations and prove the existence and uniqueness of solutions with exponential decay. This yields a globally strong convergence (with respect to the domain) of the sequence of solutions and an optimal convergence rate O ( ε 1 2 ) to the quasi-neutral...

Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis

Claire Chainais-HillairetJian-Guo LiuYue-Jun Peng — 2003

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows us to deal...

Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis

Claire Chainais-HillairetJian-Guo LiuYue-Jun Peng — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows us to deal...

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