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KIAM Preprint № 30, Moscow, 2023
Authors: Gavrikov M.B., Tayurskiy A.A.
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.
ionization oscillations, breathing modes, characteristics
Publication language: russian,  pages: 36
Research direction:
Mathematical modelling in actual problems of science and technics
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About authors:
  • Gavrikov Mikhail Borisovich, RAS
  • Tayurskiy Aleksei Aleksandrovich, RAS