Abstract
We consider a boundary value problem for a system of integro-differential equations arising when modeling the influence of an electric field on a plasma layer. The paper presents an analytical solution of this problem, which is constructed with the use of theory of the Fourier transform of generalized functions and the Gakhov–Muskhelishvili method for solving singular integral equations and the Riemann boundary value problem.
This is a preview of subscription content, log in via an institution to check access.
References
A. V. Latyshev and N. M. Gordeeva, “The behavior of plasma with an arbitrary degree of degeneracy of electron gas in the conductive layer,” Theor. Math. Phys. 192 (3), 1380–1395 (2017).
N. M. Gordeeva and A. A. Yushkanov, “Nondegenerate electron plasma in a layer in an external electric field with a mirror boundary condition,” High Temp. 56 (5), 640–647 (2018).
S. I. Bezrodnykh and N. M. Gordeeva, “Analytical solution of the system of integro-differential equations for a plasma model in an external field,” Russ. J. Math. Phys. 30 (4), 443–452 (2023).
F. D. Gakhov, Boundary Value Problems (Dover Publications, inc., New York, 1990).
M. A. Lavrentiev and B. V. Shabat, Methods of the Theory of Functions of One Complex Variable (Nauka, Moscow, 1987).
N. I. Muskhelishvili, Singular Integral Equations (Nauka, Moscow, 1968).
S. I. Bezrodnykh and V. I. Vlasov, “Singular Riemann–Hilbert problem in complex-shaped domains,” Comput. Math. Math. Phys. 54 (12), 1826–1875 (2014).
P. L. Bhatnagar, E. M. Gross, and M. Krook, “A model for collision processes in gases I. Small amplitude processes in charged and neutral one component systems,” Phys. Rev. 94 (12), 511–525 (1954).
A. S. Companeets, Course of Theoretical Physics. Vol. 2. Statistical Laws (Prosveshchenie, Moscow, 1975).
I. M. Gelfand and G. E. Shilov, Generalized Functions. Vol. 1. Properties and Operations (Academic Press, New York, 1964).
G. E. Shilov, Mathematical Analysis. The Second Special Course (Nauka, Moscow, 1965).
L. Hörmander, The Analysis of Linear Partial Differential Operators. IV. Fourier Integral Operators (Springer-Verlag, Berlin–Heidelberg–New York–Tokyo, 1985).
V. S. Vladimirov and V. V. Zharinov, Equations of Mathematical Physics (Fizmatlit, Moscow, 2000).
Funding
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
The article was submitted by the authors for the English version of the journal.
Publisher’s note. Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bezrodnykh, S.I., Gordeeva, N.M. Solution of a Boundary Value Problem for a System of Integro-Differential Equations Arising in a Model of Plasma Physics. Math Notes 114, 704–715 (2023). https://doi.org/10.1134/S000143462311007X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S000143462311007X