Geodesic
Asymptotic stability of equilibrium states for Carleman and Godunov–Sultangazin systems of equations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2019), pp. 55-57 
S. A. Dukhnovskii. Asymptotic stability of equilibrium states for Carleman and Godunov–Sultangazin systems of equations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2019), pp. 55-57. http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a8/
@article{VMUMM_2019_6_a8,
     author = {S. A. Dukhnovskii},
     title = {Asymptotic stability of equilibrium states for {Carleman} and {Godunov{\textendash}Sultangazin} systems of equations},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {55--57},
     year = {2019},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a8/}
}
TY  - JOUR
AU  - S. A. Dukhnovskii
TI  - Asymptotic stability of equilibrium states for Carleman and Godunov–Sultangazin systems of equations
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 55
EP  - 57
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a8/
LA  - ru
ID  - VMUMM_2019_6_a8
ER  - 
%0 Journal Article
%A S. A. Dukhnovskii
%T Asymptotic stability of equilibrium states for Carleman and Godunov–Sultangazin systems of equations
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 55-57
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_6_a8/
%G ru
%F VMUMM_2019_6_a8

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

One-dimensional systems of Carleman and Godunov–Sultangazin are studied for two and three groups of particles, respectively. These systems are a special case of the discrete Boltzmann kinetic equation. Theorems on existence of global solution to these systems for perturbations in the weighted Sobolev space are presented. Thus, an exponential stabilization to the equilibrium state is obtained.

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

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

[3] Vasileva O.A., Dukhnovskii S.A., “Uslovie sekulyarnosti kineticheskoi sistemy Karlemana”, Vestn. MGSU, 2015, no. 7, 33–40

[4] Dukhnovskii S.A., “O skorosti stabilizatsii reshenii zadachi Koshi dlya uravneniya Karlemana s periodicheskimi nachalnymi dannymi”, Vestn. Samar. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:1 (2017), 7–41 | DOI | Zbl

[5] Radkevich E.V., Vasil'eva O.A., Dukhnovskii S.A., “Local equilibrium of the Carleman equation”, J. Math. Sci., 207:2 (2015), 296–323 | DOI | MR | Zbl

[6] Radkevich E.V., “K probleme nesuschestvovaniya dissipativnoi otsenki dlya diskretnykh kineticheskikh uravnenii”, Vestn. Samar. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 30:1 (2013), 106–143 | DOI

[7] Radkevich E.V., “O diskretnykh kineticheskikh uravneniyakh”, Dokl. RAN, 447:4 (2012), 369–373 | MR | Zbl

[8] Vasileva O.A., “Chislennoe issledovanie sistemy uravnenii Godunova–Sultangazina. Periodicheskii sluchai”, Vestn. MGSU, 2016, no. 4, 27–35

[9] Vasil'eva O.A., Dukhnovskii S.A., Radkevich E.V., “On the nature of local equilibrium in the Carleman and Godunov–Sultangazin equations”, J. Math. Sci., 235:4 (2018), 393–453 | MR