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.
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Gavrikov M.B. and Taiurskii, A.A., Analytical solution of mixed problems for equations of one-dimensional ionization in the case of constant velocities of atoms and ions, Prepr. Keldysh Inst. Appl. Math., Moscow, 2023, no. 30.
Funding
This work was carried out with financial support from the Ministry of Science and Higher Education of the Russian Federation within the framework of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2022-283.
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Translated by V. Potapchouck
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Gavrikov, M.B., Taiurskii, A.A. Analytical Solution of Mixed Problems for the One-Dimensional Ionization Equations in the Case of Constant Velocities of Atoms and Ions. Diff Equat 59, 1332–1355 (2023). https://doi.org/10.1134/S00122661230100038
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DOI: https://doi.org/10.1134/S00122661230100038