Geodesic
Convergence of splitting method for the nonlinear Boltzmann equation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 2, pp. 123-131

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The question of convergence of the splitting method scheme for the nonlinear Boltzmann equation is considered. On the basis of the splitting method scheme, boundedness of positive solutions in the space of continuous functions is obtained. By means of the solution boundedness and found a priori estimates, convergence of the splitting method scheme and uniqueness of the limiting element are proved. The found limiting element satisfies the equivalent integral Boltzmann equation. Thereby global solvability of the nonlinear Boltzmann equation in time is shown. 
@article{SJVM_2013_16_2_a2,
     author = {A. Sh. Akysh},
     title = {Convergence of splitting method for the nonlinear {Boltzmann} equation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {123--131},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2013_16_2_a2/}
}
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A. Sh. Akysh. Convergence of splitting method for the nonlinear Boltzmann equation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 2, pp. 123-131. http://geodesic.mathdoc.fr/item/SJVM_2013_16_2_a2/