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

Peng, Yue-Jun

ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 2, pp. 295-312.

On étudie les couches limites et les limites de quasi-neutralité aux systèmes de dérivée-diffusion. On montre d’abord que cette limite est unique et déterminée par un système découplé avec données initiales et aux limites. On établit ensuite les équations des couches limites et montre l’existence et l’unicité de solutions avec l’atténuation exponentielle. Ceci implique un résultat de convergence globale (par rapport au domaine) de la suite de solutions et un taux de convergence optimale $O\left({\epsilon }^{\frac{1}{2}}\right)$ dans la limite de quasi-neutralité dans $L^2$.

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 $O\left({\epsilon }^{\frac{1}{2}}\right)$ to the quasi-neutral limit in $L^2$.

Classification : 35B25, 35B40, 35K57
Mots clés : asymptotic analysis, boundary layers, optimal convergence rate, drift-diffusion equations

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