Geodesic
Об одной задаче В. С. Владимирова в теории переноса излучения
Applications of Mathematics, Tome 29 (1984) no. 3, pp. 161-181.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper the method of spherical harmonics (MSH) is investigated, which is one of effective methods of approximative solution of the transport equation. On a unified methodical basis, boundary conditions on the outside and inner boundaries for every $P_N$-approximation of MSH are formulated. These boundary conditions coincide with Vladimirov's conditions (for $N=2r+1$) and Rumjancev's conditions (for every $N$). Symmetrization of the system of stationary equations of MSH for every $P_N$-approximation with arbitrary initial data is carried out, which extends for every $P_n$- and $P_{2r+1}$-approximation the results of V. S. Vladimirov and V. V. Smelov, respectively. The complete continuity of the resolvent of the symmetrized system is proved. On this basis the symmetrized system is solved by MSH and the convergence of approximative solutions in $W^1_2(G)$ space is proved.
DOI : 10.21136/AM.1984.104082
Classification : 35Q99, 45K05, 45L05, 82C70, 85A25
Mots-clés : method of spherical harmonics; transport equation; system of stationary equations; complete continuity; resolvent 
@article{10_21136_AM_1984_104082,
     author = {Akishev, A. Sh.},
     title = {{\CYRO}{\cyrb} {\cyro}{\cyrd}{\cyrn}{\cyro}{\cyrishrt} {\cyrz}{\cyra}{\cyrd}{\cyra}{\cyrch}{\cyre} {{\CYRV}.} {{\CYRS}.} {{\CYRV}{\cyrl}{\cyra}{\cyrd}{\cyri}{\cyrm}{\cyri}{\cyrr}{\cyro}{\cyrv}{\cyra}} {\cyrv} {\cyrt}{\cyre}{\cyro}{\cyrr}{\cyri}{\cyri} {\cyrp}{\cyre}{\cyrr}{\cyre}{\cyrn}{\cyro}{\cyrs}{\cyra} {\cyri}{\cyrz}{\cyrl}{\cyru}{\cyrch}{\cyre}{\cyrn}{\cyri}{\cyrya}},
     journal = {Applications of Mathematics},
     pages = {161--181},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {1984},
     doi = {10.21136/AM.1984.104082},
     mrnumber = {0747209},
     zbl = {0547.45010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104082/}
}
TY  - JOUR
AU  - Akishev, A. Sh.
TI  - Об одной задаче В. С. Владимирова в теории переноса излучения
JO  - Applications of Mathematics
PY  - 1984
SP  - 161
EP  - 181
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104082/
DO  - 10.21136/AM.1984.104082
LA  - ru
ID  - 10_21136_AM_1984_104082
ER  - 
%0 Journal Article
%A Akishev, A. Sh.
%T Об одной задаче В. С. Владимирова в теории переноса излучения
%J Applications of Mathematics
%D 1984
%P 161-181
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104082/
%R 10.21136/AM.1984.104082
%G ru
%F 10_21136_AM_1984_104082
Akishev, A. Sh. Об одной задаче В. С. Владимирова в теории переноса излучения. Applications of Mathematics, Tome 29 (1984) no. 3, pp. 161-181. doi : 10.21136/AM.1984.104082. http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104082/

Cité par Sources :