Abstract

We consider the main initial–boundary value (mixed) problems for the nonlinear system of one-dimensional gas ionization equations in the case of constant velocities of gas atoms and ions resulting from ionization. The atom and ion concentrations are the unknowns in this system. We find a general formula for a sufficiently smooth solution of the system. It is shown that mixed problems for the system of one-dimensional ionization equations admit integration in closed-form analytical expressions. In the case of a mixed problem for a finite interval, the analytical solution is constructed using recurrence formulas each of which is defined in a triangle belonging to some triangulation, specified in the paper, of the domain where the unknown functions are defined.

中文翻译：

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原子和离子速度恒定情况下一维电离方程混合问题的解析解

摘要

我们考虑在电离产生的气体原子和离子速度恒定的情况下一维气体电离方程非线性系统的主要初边值（混合）问题。原子和离子浓度是该系统中的未知数。我们找到了系统足够平滑的解决方案的通用公式。结果表明，一维电离方程组的混合问题允许在封闭式解析表达式中积分。对于有限区间的混合问题，解析解是使用递归公式构建的，每个递归公式都定义在属于论文中指定的未知函数定义域的某个三角剖分的三角形中。