Geodesic
Group analysis of the one-dimensional Boltzmann
Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 367-386

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

We complete the investigation of the feasibility in principle to close the moment system for the kinetic equation via invariant relations obtained by group analysis methods. For the one-dimensional equation, we obtain an affirmative answer, find an invariant closure of the moment system, and reveal several new phenomena.
Keywords: Boltzmann equation, symmetry group, kinetic equation, invariants and moment system closure. 
K. S. Platonova; A. V. Borovskikh. Group analysis of the one-dimensional Boltzmann. Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 3, pp. 367-386. http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a0/
@article{TMF_2021_208_3_a0,
     author = {K. S. Platonova and A. V. Borovskikh},
     title = {Group analysis of the one-dimensional {Boltzmann}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {367--386},
     year = {2021},
     volume = {208},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a0/}
}
TY  - JOUR
AU  - K. S. Platonova
AU  - A. V. Borovskikh
TI  - Group analysis of the one-dimensional Boltzmann
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 367
EP  - 386
VL  - 208
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a0/
LA  - ru
ID  - TMF_2021_208_3_a0
ER  - 
%0 Journal Article
%A K. S. Platonova
%A A. V. Borovskikh
%T Group analysis of the one-dimensional Boltzmann
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 367-386
%V 208
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2021_208_3_a0/
%G ru
%F TMF_2021_208_3_a0

[1] K. S. Platonova, “Gruppovoi analiz odnomernogo uravneniya Boltsmana. I. Gruppy simmetrii”, Differents. uravneniya, 53:4 (2017), 538–546 | DOI | DOI

[2] K. S. Platonova, “Gruppovoi analiz odnomernogo uravneniya Boltsmana. II. Gruppy ekvivalentnosti i gruppy simmetrii v spetsialnom sluchae”, Differents. uravneniya, 53:6 (2017), 801–813 | DOI | DOI

[3] K. S. Platonova, A. V. Borovskikh, “Gruppovoi analiz odnomernogo uravneniya Boltsmana III. Usloviya sokhraneniya fizicheskogo smysla momentnykh velichin”, TMF, 195:3 (2018), 452–483 | DOI | DOI

[4] K. S. Platonova, A. V. Borovskikh, “Gruppovoi analiz odnomernogo uravneniya Boltsmana. IV. Polnaya gruppovaya klassifikatsiya v obschem sluchae”, TMF, 201:2 (2019), 232–265 | DOI | DOI | MR

[5] K. S. Platonova, A. V. Borovskikh, “Gruppovoi analiz uravnenii Boltsmana i Vlasova”, TMF, 203:3 (2020), 417–450 | DOI | DOI | MR

[6] E. M. Nikishin, V. N. Sorokin, Ratsionalnye approksimatsii i ortogonalnost, Nauka, M., 1988 | DOI | MR

[7] V. V. Palin, E. V. Radkevich, “On the Maxwell problem”, J. Math. Sci. (N. Y.), 157:6 (2009), 816–857 | DOI | MR

[8] I. Müller, T. Ruggeri, Extended Thermodynamics, Springer Tracts in Natural Philosophy, 37, Springer, New York, 1993 | DOI | MR

[9] C. D. Levermore, “Moment closure hierarchies for kinetic theories”, J. Stat. Phys., 83:5–6 (1996), 1021–1065 | DOI | MR