An analysis of nonlinear ion transport model including diffusion and migration

The nonlocal identification problem related to nonlinear ion transport model including diffusion and migration is studied. Ion transport is assumed to be superposition of diffusion and migration under the influence of an electric field. Mathematical modeling of the experiment leads to an identification problem for a strongly nonlinear parabolic equation with nonlocal additional condition. Uniqueness of the nonlinear direct problem solution, and its continuity with respect to the total charge function is proved. An existence of a quasisolution of the identification problem is proved in the class of derived admissible coefficients. The nonlinear finite difference approximation of this problem, with an appropriate iteration algorithm, is derived. Numerical solutions of the identification problem are presented for various values of valences and diffusivities of oxidized and reduced oxidized species. The obtained results permits one to derive behaviour of the concentration and total charge depending on physical parameters.