Abstract:
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.
Key words:splitting method, convergence of the splitting method scheme, nonlinear Boltzmann equation, global solvability of the nonlinear Boltzmann equation in time, existence and uniqueness of a solution to the Boltzmann equation, a priori estimates.
Fulltext:
PDF file (193 kB)
