Variable Choices of Scaling in the Homogenization of a Nernst-Planck-Poisson Problem

Ray N, Eck C, Muntean A, Knabner P (2011)


Publication Type: Journal article

Publication year: 2011

Journal

Book Volume: 344

Pages Range: 1-32

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_RayEckMunteanKn_VarChoiOfScalInTheHomogeniOfNernstPlanPoiProblem

Abstract

We perform the periodic homogenization (i. e. e ¿ 0) of the non-stationary Nernst-Planck-Poisson system using two-scale convergence, where e is a suitable scale parameter. The objective is to investigate the influence of variable choices of scaling in e of the microscopic system of partial differential equations on the structure of the (upscaled) limit model equations. Due to the specific nonlinear coupling of the underlying equations, special attention has to be paid when passing to the limit in the electric drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained.

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APA:

Ray, N., Eck, C., Muntean, A., & Knabner, P. (2011). Variable Choices of Scaling in the Homogenization of a Nernst-Planck-Poisson Problem. The Preprint-Series of the Institute of Applied Mathematics, 344, 1-32.

MLA:

Ray, Nadja, et al. "Variable Choices of Scaling in the Homogenization of a Nernst-Planck-Poisson Problem." The Preprint-Series of the Institute of Applied Mathematics 344 (2011): 1-32.

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