caa a22 4500 469034459 CHVBK 20180323132752.0 cr unu---uuuuu 170328e19920701xx s 000 0 eng 10.1007/BF01018708 doi (NATIONALLICENCE)springer-10.1007/BF01018708 Analytic solution of boundary-value problems for nonstationary model kinetic equations [Elektronische Daten] [A. Latyshev, A. Yushkanov] A theory for constructing the solutions of boundary-value problems for nonstationary model kinetic equations is constructed. This theory was incorrectly presented in the recent well-known monographs of Cercignani [1,2]. After application of a Laplace transformation to the studied equation, separation of the variables is used, this leading to a characteristic equation. Eigenfunctions are found in the space of generalized functions, and the eigenvalue spectrum is investigated. An existence and uniqueness theorem for the expansion of the Laplace transform of the solution with respect to the eigenfunctions is proved. The proof is constructive and gives explicit expressions for the expansion coefficients. An application to the Rayleight problem is obtained, and the corresponding result of Cercignani is corrected. Plenum Publishing Corporation, 1993 Latyshev A. aut Yushkanov A. aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 92/1(1992-07-01), 782-790 0040-5779 92:1<782 1992 92 11232 https://doi.org/10.1007/BF01018708 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01018708 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Latyshev A. aut NATIONALLICENCE 700 1- Yushkanov A. aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 92/1(1992-07-01), 782-790 0040-5779 92:1<782 1992 92 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer