[Analyse d'un modèle couplé Dérive-Diffusion-Schrödinger–Poisson]
Nous présentons un système de Dérive-Diffusion-Schrödinger–Poisson qui décrit le transport d'un gaz d'électrons confiné dans une nanostructure. Nous montrons que ce système admet une unique solution. Cette preuve d'existence est obtenue à l'aide d'estimations a priori dues à la nature physique du problème et passe par la résolution d'un système quasistatique de Schrödinger–Poisson.
A Drift-Diffusion-Schrödinger–Poisson system is presented, which models the transport of a quasi bidimensional electron gas confined in a nanostructure. We prove the existence of a unique solution to this nonlinear system. The proof makes use of some a priori estimates due to the physical structure of the problem, and also involves the resolution of a quasistatic Schrödinger–Poisson system.
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@article{CRMATH_2002__335_12_1007_0,
author = {Ben Abdallah, Naoufel and M\'ehats, Florian and Vauchelet, Nicolas},
title = {Analysis of a {Drift-Diffusion-Schr\"odinger{\textendash}Poisson} model},
journal = {Comptes Rendus. Math\'ematique},
pages = {1007--1012},
publisher = {Elsevier},
volume = {335},
number = {12},
year = {2002},
doi = {10.1016/S1631-073X(02)02612-2},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02612-2/}
}
TY - JOUR AU - Ben Abdallah, Naoufel AU - Méhats, Florian AU - Vauchelet, Nicolas TI - Analysis of a Drift-Diffusion-Schrödinger–Poisson model JO - Comptes Rendus. Mathématique PY - 2002 SP - 1007 EP - 1012 VL - 335 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02612-2/ DO - 10.1016/S1631-073X(02)02612-2 LA - en ID - CRMATH_2002__335_12_1007_0 ER -
%0 Journal Article %A Ben Abdallah, Naoufel %A Méhats, Florian %A Vauchelet, Nicolas %T Analysis of a Drift-Diffusion-Schrödinger–Poisson model %J Comptes Rendus. Mathématique %D 2002 %P 1007-1012 %V 335 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02612-2/ %R 10.1016/S1631-073X(02)02612-2 %G en %F CRMATH_2002__335_12_1007_0
Ben Abdallah, Naoufel; Méhats, Florian; Vauchelet, Nicolas. Analysis of a Drift-Diffusion-Schrödinger–Poisson model. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1007-1012. doi : 10.1016/S1631-073X(02)02612-2. http://www.numdam.org/articles/10.1016/S1631-073X(02)02612-2/
[1] N. Ben Abdallah, F. Méhats, On a Vlasov–Schrödinger–Poisson system, submitted
[2] N. Ben Abdallah, F. Méhats, N. Vauchelet, in preparation
[3] On existence, uniqueness and asymptotic behavior of solutions of the basic equations for carrier transport in semiconductors, Z. Angew. Math. Mech, Volume 65 (1985) no. 2, pp. 101-108
[4] Linear and Quasi-Linear Equations of Parabolic Type, Transl. Math. Monographs, American Mathematical Society, 1988
[5] Semiconductor Equations, Springer-Verlag, Vienna, 1990
[6] A stationary Schrödinger–Poisson system arising from the modelling of electronic devices, Forum Math, Volume 2 (1990) no. 5, pp. 489-510
[7] Inverse Spectral Theory, Academic Press, 1987
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