Analytical Solution of the Mixed Problem on a Segment for One-dimensional Ionization Equations in the Case of Constant Velocities of Atoms and Ions

In this paper, the main initial-boundary (mixed) problems for a nonlinear system of equations of one-dimensional gas ionization in the case of constant velocities of gas atoms and ions arising as a result of ionization are presented. The concentrations of atoms \((n_{a})\) and ions \((n_{i})\) are unknowns in this system. A general formula for a sufficiently smooth solution of the \(n_{a}(t,z)\) , \(n_{i}(t,z)\) of this system, where \(t\) is time and \(z\) is a spatial coordinate, is found. In the case of a mixed problem for a finite interval, the analytic solution is constructed by means of recurrence formulas, each of which is defined in a triangle belonging to some triangulation of the region of definition of the unknown functions specified in the paper.