Geodesic
Symmetries and invariant solutions of the~one-dimensional Boltzmann equation for inelastic collisions
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 221-229

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We consider the one-dimensional integro-differential Boltzmann equation for Maxwell particles with inelastic collisions. We show that the equation has a five-dimensional algebra of point symmetries for all dissipation parameter values and obtain an optimal system of one-dimensional subalgebras and classes of invariant solutions.
Keywords: inelastic Boltzmann equation, Lie symmetry
Mots-clés : invariant solution, optimal system of subalgebras. 
@article{TMF_2016_186_2_a2,
     author = {O. V. Ilyin},
     title = {Symmetries and invariant solutions of the~one-dimensional {Boltzmann} equation for inelastic collisions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {221--229},
     publisher = {mathdoc},
     volume = {186},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a2/}
}
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O. V. Ilyin. Symmetries and invariant solutions of the~one-dimensional Boltzmann equation for inelastic collisions. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 221-229. http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a2/