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

Published online by Cambridge University Press:  15 April 2002

Yue-Jun Peng
Yue-Jun Peng*
Affiliation:
Laboratoire de Mathématiques Appliquées, CNRS UMR 6620, Université Blaise Pascal (Clermont-Ferrand 2), 63177 Aubière Cedex, France, and, The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin NT, Hong Kong.
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Abstract

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 $O(\varepsilon^\frac{1}{2})$ to the quasi-neutral limit in L2.

Keywords

Asymptotic analysisboundary layersoptimal convergence ratedrift-diffusion equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 2 , March 2001 , pp. 295 - 312
Copyright
© EDP Sciences, SMAI, 2001

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