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 and ions are unknowns in this system....

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2024, Vol.45 (1), p.39-49
Main Authors: Gavrikov, M. B., Taiurskii, A. A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Exact solutions
Gas ionization
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Nonlinear systems
Probability Theory and Stochastic Processes
Triangulation
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Summary: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 and ions are unknowns in this system. A general formula for a sufficiently smooth solution of the , of this system, where is time and 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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224010177