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

Yue-Jun Peng

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 35, Issue: 2, page 295-312
  • ISSN: 0764-583X

Abstract

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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 limit in L2.

How to cite

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Peng, Yue-Jun. "Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations." ESAIM: Mathematical Modelling and Numerical Analysis 35.2 (2010): 295-312. <http://eudml.org/doc/197394>.

@article{Peng2010,
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. },
author = {Peng, Yue-Jun},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Asymptotic analysis; boundary layers; optimal convergence rate; drift-diffusion equations.; asymptotic analysis; mixed boundary conditions},
language = {eng},
month = {3},
number = {2},
pages = {295-312},
publisher = {EDP Sciences},
title = {Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations},
url = {http://eudml.org/doc/197394},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Peng, Yue-Jun
TI - Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 2
SP - 295
EP - 312
AB - 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.
LA - eng
KW - Asymptotic analysis; boundary layers; optimal convergence rate; drift-diffusion equations.; asymptotic analysis; mixed boundary conditions
UR - http://eudml.org/doc/197394
ER -

References

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