POISSON-NERNST-PLANCK MODELS FOR THREE ION SPECIES: MONOTONIC PROFILES VS. OSCILLATORY PROFILES

We consider ionic flows through an ion channel via a quasi-one-dimensional classical Poisson-Nernst-Planck model. The specific biological setup involves ionic solutions with three ion species and the permanent charge is set to be zero. It is known that, for ionic flows with two ion species, the spatial profiles of the electric potential and the ion concentrations are monotonic, independent of boundary conditions. For ionic flows with three or more ion species with at least three different valences, depending on the boundary conditions, the profiles could be oscillatory. In this work, for ionic mixtures with two cation species of different valences and one anion species, we will provide a complete classification in terms of boundary conditions on when the profiles are monotonic and when they are oscillatory. This would be an important step for studies including nonzero permanent charges.