Homogenization of a nonlinear drift-diffusion system for multiple charged species in a porous medium
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 non...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
15 June 2022
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| In: |
Nonlinear analysis. Real world applications
Year: 2022, Volume: 68, Pages: 1-28 |
| DOI: | 10.1016/j.nonrwa.2022.103651 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.nonrwa.2022.103651 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S1468121822000797 
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| Author Notes: | Apratim Bhattacharya, Markus Gahn, Maria Neuss-Radu |
| Summary: | 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 ε 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∞-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 ε→0 for different scalings of the microscopic model. |
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| Item Description: | Gesehen am 27.07.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.1016/j.nonrwa.2022.103651 |