Abstract.A singular perturbation problem, modeling one-dimensional time-dependent electrodiffusion of ions (holes and electrons) in a bipolar membrane (semi-conductor diode) at a reverse bias is analyzed for galvanostatic (fixed electric current) conditions. It is shown that, as the perturbation parameter tends to zero, the solution of the perturbed problem tends to the solution of a limiting problem which is, depending on the input data, either a conventional bipolar electrodiffusion problem or a particular electrodiffusional time-dependent free boundary problem. In both cases, the properties of the limiting solution are analyzed, along with those of the respective boundary and transition layer solutions.
Introduction.In our recent paper [1] we analyzed the electrodiffusional free boundary problem that arose asymptotically in the singularly perturbed model of electrodialysis for a vanishing perturbation parameter.This model concerned the passage of a specified direct electric current through a layer of univalent electrolyte adjacent to the wall (cathode, cation exchange membrane) selectively permeable to positive ions (cations) only. The simplest version of the governing equations was t > 0: pf = {p£x +pe4>%)x Vx€(0,l), Here p£(x,t), n£(x,t), cp£(x,t) are, respectively, the cation and anion (negative ions) concentrations and the electric potential. Equations (0.1) and (0.2) are the Nernst-Planck