Geodesic
Study of spatial relaxation by means of solving a kinetic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 1, pp. 131-141 
V. V. Aristov; M. V. Panyashkin. Study of spatial relaxation by means of solving a kinetic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 1, pp. 131-141. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a9/
@article{ZVMMF_2011_51_1_a9,
     author = {V. V. Aristov and M. V. Panyashkin},
     title = {Study of spatial relaxation by means of solving a~kinetic equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {131--141},
     year = {2011},
     volume = {51},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a9/}
}
TY  - JOUR
AU  - V. V. Aristov
AU  - M. V. Panyashkin
TI  - Study of spatial relaxation by means of solving a kinetic equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 131
EP  - 141
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a9/
LA  - ru
ID  - ZVMMF_2011_51_1_a9
ER  - 
%0 Journal Article
%A V. V. Aristov
%A M. V. Panyashkin
%T Study of spatial relaxation by means of solving a kinetic equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 131-141
%V 51
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a9/
%G ru
%F ZVMMF_2011_51_1_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

Nonuniform spatial relaxation is studied by solving a kinetic equation. Both analytical and numerical methods are used in the study. The collision term is used in a model form that makes it possible to find conditions for the nonequilibrium boundary function that ensure anomalous transport of nonequilibrium momentum and energy. Specifically, the temperature gradient has the same sign as the heat flux, but this does not contradict the traditional macroscopic description, since relaxation occurs in a zone of the order of the mean free path. Versions of such nonequilibrium heating or cooling in a downstream region are presented.

[1] Aristov V. V., Cheremisin F. G., Pryamoe chislennoe reshenie kineticheskogo uravneniya Boltsmana, VTs RAN, M., 1992 | MR

[2] Aristov V. V., Direct methods of solving the Boltzmann equation and study of nonequilibrium flows, Kluwer Acad. Publ., Dordrecht, 2001 | MR | Zbl

[3] Kogan M. N., Dinamika razrezhennogo gaza, Nauka, M., 1967

[4] Cherchinyani K., Matematicheskie metody v kineticheskoi teorii gazov, Mir, M., 1973 | MR

[5] Fertsiger Dzh., Kaper G., Matematicheskaya teoriya protsessov perenosa v gazakh, Mir, M., 1976

[6] Aristov V. V., “Steady state, supersonic flow solution of the Boltzmann equation”, Phys. Letts A, 250 (1998), 354–359 | DOI

[7] Aristov V. V., Zabelok S. A., Frolova A. A., “Neravnovesnye protsessy perenosa v zadachakh o neodnorodnoi relaksatsii”, Matem. modelirovanie, 21:12 (2009), 59–75 | Zbl

[8] Aristov V. V., Frolova A. A., Zabelok S. A., “A new effect of the nongradient transport in relaxation zones”, Letts J. Exploring Frontiers Phys., 88 (2009), 30012

[9] Shakhov E. M., Metod issledovaniya dvizhenii razrezhennogo gaza, Nauka, M., 1974