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Solutions of discrete-velocity Boltzmann equations via Bateman and Riccati equations. (English. Russian original) Zbl 1031.82042
Theor. Math. Phys. 131, No. 2, 595-608 (2002); translation from Teor. Mat. Fiz. 131, No. 2, 179-193 (2002).
Summary: We propose several approaches for solving two discrete-velocity Boltzmann equations using the rescaling ansatz and the truncated Painlevé expansions. We use solutions of the two- and three-dimensional Bateman equations for the singularity manifold conditions to reduce the problem to Riccati equations. Both equations fail the Painlevé test.

82C40 Kinetic theory of gases in time-dependent statistical mechanics
35B25 Singular perturbations in context of PDEs
35F20 Nonlinear first-order PDEs
35L40 First-order hyperbolic systems
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