Convergence of a splitting method for the nonlinear Boltzmann equation

A.Sh. Akysh

2013

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DOI 10.1134/s1995423913020031
Data confidence 70 medium
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Abstract

Convergence of a splitting method scheme for the nonlinear Boltzmann equation is considered. Using the splitting method scheme, boundedness of the positive solutions in a space of continuous functions is obtained. By means of the solution boundedness and some a priori estimates, convergence of the splitting method scheme and uniqueness of the limiting element are proved. The limiting element satisfies an equivalent integral Boltzmann equation. Thereby global in time solvability of the nonlinear Boltzmann equation is shown.