About the choice of methods for solving Poisson's equation in the general case of the distribution of the volume charge density and about the formulation of boundary conditions in electrokinetic problems (review)

We consider the situation when the distribution of the space charges in the Poisson equation differs from the Boltzmann distribution. This required the usage of the theory of correctly solution of boundary value problems for equations of Laplace and Poisson. The most general methods for solving these tasks were used. Boundary conditions, used in electrokinetic phenomena, were considered. Closed system of equations, which allow to model mathematically the electrokinetic processes in the absence of thermodynamic equilibrium, was presented.