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Approximate biflow solutions of the kinetic Bryan-Pidduck equation. (English) Zbl 0962.76084
Summary: We obtain some explicit approximate solutions for the nonlinear Bryan-Pidduck equation (that is the Boltzmann equation for the model of rough spheres). The solutions have a form of spatially nonhomogeneous linear combination of two global Maxwellians with zero mass angular velocities, but arbitrary mass linear velocities. We also find low-temperature asymptotics of uniform-integral and pure integral errors for Bryan-Pidduck equation. Sufficient conditions for the infinitesimality of these errors are obtained, which are based on some assumptions imposed on coefficient functions and parameters of distribution.

MSC:
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
45K05 Integro-partial differential equations
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