Relativistic centered wave of compression
Matematičeskoe modelirovanie, Tome 19 (2007) no. 6, pp. 43-52.

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

The problem relativistic isentropic compression by a plain piston of substance with a power equation of state is reduced to self-similar state and it is solved. Thereby the relativistic centered wave of compression is constructed. The numerical and approximate solutions in ultrarelativistic and nonrelativistic limits are received. The features, which carry the relativistic dynamics at transition to limiting compression, are considered. The evolutions of space and time dependences on the piston are described. The estimations of time of transition are resulted in relativistic limit in cylindrical and spherical geometry.
@article{MM_2007_19_6_a3,
     author = {V. V. Prut},
     title = {Relativistic centered wave of compression},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {43--52},
     publisher = {mathdoc},
     volume = {19},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_6_a3/}
}
TY  - JOUR
AU  - V. V. Prut
TI  - Relativistic centered wave of compression
JO  - Matematičeskoe modelirovanie
PY  - 2007
SP  - 43
EP  - 52
VL  - 19
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2007_19_6_a3/
LA  - ru
ID  - MM_2007_19_6_a3
ER  - 
%0 Journal Article
%A V. V. Prut
%T Relativistic centered wave of compression
%J Matematičeskoe modelirovanie
%D 2007
%P 43-52
%V 19
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2007_19_6_a3/
%G ru
%F MM_2007_19_6_a3
V. V. Prut. Relativistic centered wave of compression. Matematičeskoe modelirovanie, Tome 19 (2007) no. 6, pp. 43-52. http://geodesic.mathdoc.fr/item/MM_2007_19_6_a3/

[1] Kalitkin N. N., Kuzmina L. V., Funtikov A. I., “Glavnye udarnye adiabaty 10 metallov”, Matem. modelirovanie, 14:10 (2002), 27–42 | Zbl

[2] Fortov V. E. i dr. (red.), Udarnye volny i ekstremalnye sostoyaniya veschestva, Nauka, M., 2000

[3] Zababakhin E. I., Zababakhin I. E., Yavleniya neogranichennoi kumulyatsii, Nauka, M., 1988

[4] Stanyukovich K. P., Neustanovivshiesya dvizheniya sploshnoi sredy, Nauka, M., 1971 | MR

[5] Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987 | MR

[6] Barenblatt G. I., Podobie, avtomodelnost, promezhutochnaya asimptotika, Gidrometeoizdat, Leningrad, 1982 | MR

[7] Volosevich P. P., Levanov E. I., Fetisov S. A., Avtomodelnye resheniya zadach nagreva i dinamiki plazmy, MFTI, M., 2001

[8] Demchenko V. V., “Sravnitelnoe issledovanie nekotorykh gidrodinamicheskikh protsessov szhatiya”, ZhVMMF, 19:2 (1979), 540–545

[9] Bautin S. P., “Matematicheskoe issledovanie bezudarnogo szhatiya gaza”, Uspekhi mekhaniki, 1:1 (2002), 3–36 | MR

[10] Bautin S. P., Matematicheskaya teoriya silnogo bezudarnogo szhatiya idealnogo gaza, Nauka, Novosibirsk, 1997

[11] Prut V. V., “Avtomodelnoe izentropicheskoe szhatie veschestva”, ZhVMMF, 41:2 (2001), 327–341 | Zbl

[12] Marti J. M., Muller E., “Extension of the piecewise parabolic method to one-dimensional relativistic hydrody-namics”, J. Comput. Physics, 123:1 (1996), 1–14 | DOI | MR | Zbl

[13] Landau L. D., Lifshits E. M., Teoreticheskaya fizika. Gidrodinamika, Nauka, M., 1986 | MR

[14] Taub A. H., “Relativistic Rankine–Hugoniot Equations”, Phys. Rev., 74:3 (1948), 328–334 | DOI | MR | Zbl

[15] Shapiro S. L., Teukolsky S. A., Black holes, white drafts, and neutron stars, Wiley, NY, 1983; Shapiro S. L., Tyukolski S., Chernye dyry, belye karliki i neitronnye zvezdy, t. 1, Mir, M., 1985 ; т. 2 | MR

[16] Zeldovich Ya. B., Novikov I. D., Teoriya tyagoteniya i evolyutsiya zvezd, Nauka, M., 1971