Homogenization of the Generalized Poisson-Nernst-Planck Problem in Two-Phase Medium: the Corrector Due to Nonlinear Interface Condition

摘要

The paper deals with homogenization of the generalized Poisson-Nernst-Planck problem stated in the disconnected domain composed of solid and pore phases. The nonlinear cross-diffusion transport equations are coupled with the Stokes flow model. At the interface between two phases, field variables are discontinuous allowing jumps, and nonlinear interface conditions describing electro-chemical reactions are taken into consideration. The first-order asymptotic corrector corresponding to the non-periodic interface data is derived rigorously and justified by residual error estimates within the homogenization procedure.