  In this paper, we study effects of permanent charges on ion flows through
membrane channels via a quasi-one-dimensional classical Poisson-Nernst-Planck
system. This system includes three ion species, two cations with different
valences and one anion, and permanent charges with a simple structure, zeros at
the two end regions and a constant over the middle region. For small permanent
charges, our main goal is to analyze the effects of permanent charges on ionic
flows, interacting with the boundary conditions and channel structure.
Continuing from a previous work, we investigate the problem for a new case
toward a more comprehensive understanding about effects of permanent charges on
ionic fluxes.
