Nonlinear Initial-Boundary-Value Problem for Convection, Diffusion, Ionization, and Recombination Processes

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Abstract
The time‐dependent convection‐diffusion equation with ionization and recombination reactions is reduced by means of a nonlinear transformation to a differential equation, in which the nonlinear term represents a small perturbation. The general procedure of solution for the corresponding nonlinear initial‐boundary‐value problem is then established by means of the method of successive approximations. Uniqueness and convergence of the analytical solution are discussed. As applications, the temporal change of an initial distribution of electrons and ions is discussed for a finite box system and an infinitely extended system, respectively.