Homogenization of a nonlinear drift-diffusion system for multiple charged species in a porous medium

Bhattacharya A, Gahn M, Neuss-Radu M (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Nonlinear Analysis-Real World Applications Elsevier

Book Volume: 68

DOI: 10.1016/j.nonrwa.2022.103651

Abstract

We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's equation for the electric potential. The diffusion terms depend nonlinearly on the concentrations. We consider non-homogeneous Neumann boundary condition for the electric potential. The aim is the rigorous derivation of an effective (homogenized) model in the limit when the scale parameter epsilon tends to zero. This is based on uniform a priori estimates for the solutions of the microscopic model. The crucial result is the uniform L-infinity-estimate for the concentration in space and time. This result exploits the fact that the system admits a nonnegative energy functional which decreases in time along the solutions of the system. By using weak and strong (two-scale) convergence properties of the microscopic solutions, effective models are derived in the limit epsilon -> 0 for different scalings of the microscopic model. (C) 2022 Elsevier Ltd. All rights reserved.

Authors with CRIS profile

Apratim Bhattacharya Naturwissenschaftliche Fakultät Maria Neuß Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Ruprecht-Karls-Universität Heidelberg

Germany (DE)

How to cite

APA:

Bhattacharya, A., Gahn, M., & Neuss-Radu, M. (2022). Homogenization of a nonlinear drift-diffusion system for multiple charged species in a porous medium. Nonlinear Analysis-Real World Applications, 68. https://doi.org/10.1016/j.nonrwa.2022.103651

MLA:

Bhattacharya, Apratim, Markus Gahn, and Maria Neuss-Radu. "Homogenization of a nonlinear drift-diffusion system for multiple charged species in a porous medium." Nonlinear Analysis-Real World Applications 68 (2022).

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