  In order to describe the dynamics of crowded ions (charged particles), we use
an energetic variation approach to derive a modified Poisson-Nernst-Planck
(PNP) system which includes an extra dissipation due to the effective velocity
differences between ion species. Such a system is more complicated than the
original PNP system but with the same equilibrium states. Using Schauder's
fixed-point theorem, we develop a local existence theorem of classical
solutions for the modified PNP system. Different dynamics (but same equilibrium
states) between the original and modified PNP systems can be represented by
numerical simulations using finite element method techniques.
