Abstract
<abstract> We study a one-dimensional Poisson-Nernst-Planck system for ionic flows through membrane channels with two ion species, one positively charged and one negatively charged. Nonzero but small permanent charges are included. The cross-section area of the channel is included in the system, which provides certain information of the geometry of the three-dimensional channel. This is crucial for our analysis. Of particular interest is to analyze the qualitative properties of the individual fluxes with partial neutral boundary conditions, which provides complementary insights and better understanding of the ionic flow properties. Our study shows that the individual fluxes depend sensitively on multiple system parameters such as permanent charges, channel geometry, boundary conditions (concentrations and potentials) and boundary layers caused by the violation of electroneutrality conditions. Numerical simulations are further performed to provide a more intuitive illustration of our analytical results, and it turns out that numerical results are consistent with our analytical ones. </abstract>
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