Boundary value problem (BVP) of Poisson-Nernst-Planck (PNP) systems with local excess potentials are extensively analyzed and simulated. For PNP systems with nonlocal excess potentials, on the other hand, even the issue
of well-posedness of the BVP is poorly understood. PNP systems with nonlocal excess potentials can be viewed as functional di erential systems with in nite degree of freedoms and the BVP with the traditional two-point-boundary-conditions" would be severely under determined. We propose a natural \boundary condition" for PNP systems with nonlocal excess potentials in a relatively simple setting and show the BVP is generally well-posed.