Parabolic-elliptic system modeling biological ion channels (Q2034012)

A system of parabolic equations describing transport of biological ions in one-dimensional channels, coupled through an elliptic equation for the potential, is considered. This system of Nernst-Planck-Poisson type is supplemented with biologically relevant boundary conditions of Chang-Jaffé type (the normal component of the flux is proportional to the weighted difference of concentrations across the boundary). The existence, regularity and positivity properties of local in time solutions are established.