Abstract:
The one-dimensional system of Vlasov equations linearized at the stationary solution of the nonlinear system is considered. A rigorous theory of Landau damping is presented. A new integral equation with a shift for the electric field is derived in a more general case, and the uniqueness of its solution is proved. A quasiclassical approximation for the linear system of Vlasov equations is obtained.
Bibliography: 15 titles.
\Bibitem{MasFed85}
\by V.~P.~Maslov, M.~V.~Fedoryuk
\paper The linear theory of Landau damping
\jour Math. USSR-Sb.
\yr 1986
\vol 55
\issue 2
\pages 437--465
\mathnet{http://mi.mathnet.ru/eng/sm2007}
\crossref{https://doi.org/10.1070/SM1986v055n02ABEH003013}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=806510}
\zmath{https://zbmath.org/?q=an:0662.35035|0589.35042}
Linking options:
https://www.mathnet.ru/eng/sm2007
https://doi.org/10.1070/SM1986v055n02ABEH003013
https://www.mathnet.ru/eng/sm/v169/i4/p445
This publication is cited in the following 21 articles:
S. A. Stepin, A. G. Tarasov, “Dispersion relation in the kinetic model of collisionless plasma”, Theoret. and Math. Phys., 210:3 (2022), 386–397
Stepin S.A., “Dispersion Relationship and Spectrum in the Collisionless Plasma Kinetic Model”, Russ. J. Math. Phys., 28:1 (2021), 107–120
Valery V. Kozlov, “Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems”, Regul. Chaotic Dyn., 25:6 (2020), 674–688
S. A. Stepin, “Schur complement and continuous spectrum in a kinetic plasma model”, Dokl. Math., 101:3 (2020), 231–234
A. L. Skubachevskii, Y. Tsuzuki, “Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space”, Comput. Math. Math. Phys., 57:3 (2017), 541–557
A. L. Skubachevskii, “Nonlocal Problems for the Vlasov–Poisson Equations in an Infinite Cylinder”, Funct. Anal. Appl., 49:3 (2015), 234–238
Carlo Lancellotti, “On the Glassey-Schaeffer Estimates for Linear Landau Damping”, Journal of Computational and Theoretical Transport, 44:4-5 (2015), 198
A. L. Skubachevskii, “Vlasov–Poisson equations for a two-component plasma in a homogeneous magnetic field”, Russian Math. Surveys, 69:2 (2014), 291–330
Barre J., Yamaguchi Y.Y., “On Algebraic Damping Close to Inhomogeneous Vlasov Equilibria in Multi-Dimensional Spaces”, J. Phys. A-Math. Theor., 46:22 (2013), 225501
R.E. Heath, I.M. Gamba, P.J. Morrison, C. Michler, “A discontinuous Galerkin method for the Vlasov–Poisson system”, Journal of Computational Physics, 2011
Barre J., Olivetti A., Yamaguchi Y.Y., “Algebraic Damping in the One-Dimensional Vlasov Equation”, J. Phys. A-Math. Theor., 44:40 (2011), 405502
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