| Abstract: |
| We derive a homogenized model for the multi-species Poisson-Nernst-Planck (PNP) equations defined on a periodic porous medium. This extends the previous homogenization results for the PNP equations concerning two species. Here, the main difficulty is that the microscopic concentrations remain uniformly bounded in a space with relatively weak regularity. Therefore, the standard Aubin-Lions-Simon type compactness results for porous media, which give strong convergence of the microscopic solutions, become inapplicable in our weak setting. We overcome this problem by a new approach involving cut-off functions. |
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