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About the splitting algorithm for Boltzmann and B.G.K. equations. (English) Zbl 0876.35088
The authors prove the convergence of splitting algorithms for transport and collision operators for Boltzmann and B.G.K. equations. The work is based on the new proofs (P. L. Lions, E. Ringeissen) of the existence for both equations, since they are better-adapted to the method of splitting. There remains a technical difficulty that is solved here: the so-called velocity average compactness lemmas cannot be applied here, and the authors prove a discrete version adapted to the splitting method. This uses the Duhamel formula of a transport equation, interpolation theory to put the problem in an $$L^2$$ framework and a Poisson formula in order to control the high frequencies of the velocity averaging of the splitting solution.