Geodesic
Group analysis of the~one-dimensional Boltzmann equation: IV.~Complete group classification in the~general case
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 232-265

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

We consider the one-dimensional Boltzmann equation $f_t+cf_x+(\mathcal{F} f)_c=0$ with a function $\mathcal{F}$ depending on $(t,x,c,f)$ and obtain the complete group classification of such equations in the class of point changes of whole set of variables $(t,x,c,f)$. For this, we impose additional conditions on the transformations for the invariance of (a) the relations $dx=c\,dt$ and $dc=\mathcal{F}\,dt$, (b) the lines $dt=dx=0$, and (c) the form $f\,dx\,dc$, which fix the physical meaning of the used variables and the relations between them.
Keywords: Boltzmann equation, symmetry group, gas dynamics equation.
Mots-clés : equivalence group 
@article{TMF_2019_201_2_a6,
     author = {A. V. Borovskikh and K. S. Platonova},
     title = {Group analysis of the~one-dimensional {Boltzmann} equation: {IV.~Complete} group classification in the~general case},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {232--265},
     publisher = {mathdoc},
     volume = {201},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a6/}
}
TY  - JOUR
AU  - A. V. Borovskikh
AU  - K. S. Platonova
TI  - Group analysis of the~one-dimensional Boltzmann equation: IV.~Complete group classification in the~general case
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 232
EP  - 265
VL  - 201
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a6/
LA  - ru
ID  - TMF_2019_201_2_a6
ER  - 
%0 Journal Article
%A A. V. Borovskikh
%A K. S. Platonova
%T Group analysis of the~one-dimensional Boltzmann equation: IV.~Complete group classification in the~general case
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 232-265
%V 201
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a6/
%G ru
%F TMF_2019_201_2_a6
A. V. Borovskikh; K. S. Platonova. Group analysis of the~one-dimensional Boltzmann equation: IV.~Complete group classification in the~general case. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 2, pp. 232-265. http://geodesic.mathdoc.fr/item/TMF_2019_201_2_a6/