Centrally symmetric steady states in a model of electrodiffusion

We study the centrally symmetric mathematical model of electrodiffusion. This model describes in particular the transport of the $Li^+$ ions in certain electrochemical current sources. We demonstrate that the steady state solution of the considered model exists and is unique if the boundary values of the ion concentration and electric potential are given. This solution also proves to be the stable attractor of the time-dependent solutions with different initial value distributions.