Geodesic
On the large-time behavior of solutions to the Cauchy problem for a~$2$-dimensional discrete kinetic equation
Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 3, Tome 47 (2013), pp. 108-139.

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

Existence of global solution for a $2$-dimensional discrete equation of kinetics and expansion with respect to smoothness are obtained, and the effect of progressing waves generated by the operator of interaction is investigated. 
@article{CMFD_2013_47_a6,
     author = {E. V. Radkevich},
     title = {On the large-time behavior of solutions to the {Cauchy} problem for a~$2$-dimensional discrete kinetic equation},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {108--139},
     publisher = {mathdoc},
     volume = {47},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2013_47_a6/}
}
TY  - JOUR
AU  - E. V. Radkevich
TI  - On the large-time behavior of solutions to the Cauchy problem for a~$2$-dimensional discrete kinetic equation
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2013
SP  - 108
EP  - 139
VL  - 47
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2013_47_a6/
LA  - ru
ID  - CMFD_2013_47_a6
ER  - 
%0 Journal Article
%A E. V. Radkevich
%T On the large-time behavior of solutions to the Cauchy problem for a~$2$-dimensional discrete kinetic equation
%J Contemporary Mathematics. Fundamental Directions
%D 2013
%P 108-139
%V 47
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2013_47_a6/
%G ru
%F CMFD_2013_47_a6
E. V. Radkevich. On the large-time behavior of solutions to the Cauchy problem for a~$2$-dimensional discrete kinetic equation. Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 3, Tome 47 (2013), pp. 108-139. http://geodesic.mathdoc.fr/item/CMFD_2013_47_a6/

[1] Vedenyapin V. V., Kineticheskie uravneniya Boltsmana i Vlasova, Fizmatlit, M., 2001

[2] Godunov S. K., Sultangazin U. M., “O diskretnykh modelyakh kineticheskogo uravneniya Boltsmana”, Usp. mat. nauk, 26:3(159) (1971), 3–51 | MR | Zbl

[3] Radkevich E. V., Matematicheskie aspekty neravnovesnykh protsessov, Izd-vo Tamary Rozhkovskoi, Novosibirsk, 2007

[4] Radkevich E. V., “O suschestvovanii globalnykh reshenii zadachi Koshi dlya diskretnykh kineticheskikh uravnenii”, Probl. mat. analiza, 62, 2011, 109–151

[5] Radkevich E. V., “O prirode nesuschestvovaniya dissipativnoi otsenki dlya diskretnykh kineticheskikh uravnenii”, Probl. mat. analiza, 69, 2013 (to appear)

[6] Babin A. V., Ilyin A. A., Titi E. S., “On the regularization mechanism for the periodic KdV equation”, Comm. Pure Appl. Math., 64 (2011), 0591–0648 | DOI | MR

[7] Boltzmann L., “On the Maxwell method to the reduction of hydrodynamic equations from the kinetic gas theory”, The L. Boltzmann Memories, Rep. Brit. Assoc., 1894, v. 2, ed. O. V. Kuznetsov, Nauka, M., 1984, 307–321 (in Russian)

[8] Broadwell T. E., “Study of rarified shear flow by the discrete velocity method”, J. of Fluid Mechanics, 19:3 (1964), 401–414 | DOI | MR | Zbl

[9] Chapman S., Cowling T., Mathematical theory of non-uniform gases, Cambridge University Press, Cambridge, 1970 | MR

[10] Chen G. Q., Levermore C. D., Lui T.-P., “Hyperbolic conservation laws with stiff relaxation terms and entropy”, Commun. Pure Appl. Math., 47:6 (1994), 787–830 | DOI | MR | Zbl

[11] Palin V. V., Radkevich E. V., “Mathematical aspects of the Maxwell problem”, Applicable Analysis, 88:8 (2009), 1233–1264 | DOI | MR | Zbl

[12] Radkevich E. V., “The existence of global solutions to the Cauchy problem for discrete kinetic equations. II”, J. Math. Sci. (N. Y.), 181:5 (2012), 701–750 | DOI | MR | Zbl