Analytical solution of mixed problems for one-dimensional ionization equations in the case of constant velocities of atoms and ions
The main initial-boundary (mixed) problems are considered for a nonlinear system of equations for one-dimensional gas ionization in the case of constant velocities of gas atoms and ions arising as a result of ionization. The unknowns in this system are the concentrations of atoms and ions. A general formula is found for a sufficiently smooth solution of this system depending on time and spatial coordinate. It is shown that mixed problems for the system of one-dimensional ionization equations admit integration in the form of explicit analytical expressions. In the case of a mixed problem for a finite segment, an analytical solution is constructed using recursive formulas, each of which is defined in a triangle belonging to some domain of definition of unknown functions indicated in the triangulation work.