Abstract:
For the example of the Fokker–Planck equation with arbitrary coefficients, asymptotic (with respect to the time) solutions of linear kinetic equations are constructed by means of the formalism of Green's functions as well as by the method of quasistationary distribution functions. An expression is obtained for the eigenvalue of minimal absolute magnitude and the corresponding eigenfunction. An algorithm is given for calculating the following eigenvalues. Over a finite interval, the asymptotic solutions found for the Fokker–Planck equation coincide. The method of quasistationary distribution functions is more general than the methods using eigenvalues and eigenfunctions.
Citation:
S. A. Reshetnyak, S. M. Kharchev, L. A. Shelepin, “Asymptotic methods in the theory of linear kinetic equations”, TMF, 49:1 (1981), 131–139; Theoret. and Math. Phys., 49:1 (1981), 934–940
\Bibitem{ResKhaShe81}
\by S.~A.~Reshetnyak, S.~M.~Kharchev, L.~A.~Shelepin
\paper Asymptotic methods in the theory of linear kinetic equations
\jour TMF
\yr 1981
\vol 49
\issue 1
\pages 131--139
\mathnet{http://mi.mathnet.ru/tmf2521}
\transl
\jour Theoret. and Math. Phys.
\yr 1981
\vol 49
\issue 1
\pages 934--940
\crossref{https://doi.org/10.1007/BF01019127}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981NT81100011}
Linking options:
https://www.mathnet.ru/eng/tmf2521
https://www.mathnet.ru/eng/tmf/v49/i1/p131
This publication is cited in the following 3 articles:
S. A. Reshetnyak, L. A. Shelepin, V. A. Shcheglov, “Gasdynamic lasers. Kinetics of processes ahead of the nozzle”, J Russ Laser Res, 14:6 (1993), 426
S. A. Reshetnyak, L. A. Shelepin, “Kramers' theory for three-atom reactions”, Theor Exp Chem, 19:4 (1984), 369
V.N. Sazonov, I.E. Khromov, “On the statistics of an ensemble of oscillators under excitation. IV. Evaluation of the time for kinetic excitation into the quasicontinuum based on Kramers' theory”, Chemical Physics, 76:1 (1983), 25
Citation in format AMSBIB
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