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Analytical Solution of Mixed Problems for the One-Dimensional Ionization Equations in the Case of Constant Velocities of Atoms and Ions
- Authors: Gavrikov M.B1, Tayurskiy A.A1,2
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Affiliations:
- Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia
- Bauman Moscow State Technical University, Moscow, 105005, Russia
- Issue: Vol 59, No 10 (2023)
- Pages: 1335-1356
- Section: Articles
- URL: https://rjmseer.com/0374-0641/article/view/649462
- DOI: https://doi.org/10.31857/S0374064123100035
- EDN: https://elibrary.ru/ONCTCE
- ID: 649462
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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.
About the authors
M. B Gavrikov
Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia
Email: mbgavrikov@yandex.ru
Москва, Россия
A. A Tayurskiy
Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia; Bauman Moscow State Technical University, Moscow, 105005, Russia
Author for correspondence.
Email: tayurskiy2001@mail.ru
Москва, Россия
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