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Pettersson, R.

On boundedness of higher velocity moments for the linear Boltzmann equation with diffuse boundary conditions. (English) Zbl 1274.82049

Transp. Theory Stat. Phys. 41, No. 5-6, 345-355 (2012).
Author’s abstract: This article considers the time and space-dependent linear Boltzmann equation for elastic or inelastic (granular) collisions. First, in the angular cut-off case or with hard sphere collisions, mild \(L^1\)-solutions are constructed as limits of iterate functions. Then, in the case of hard potentials together with diffuse boundary conditions, global boundedness in time of higher velocity moments is proved, using our old collision velocity estimates together with a Jensen inequality.
Reviewer: Oleg A. Sinkevich (Moskva)

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
35Q20 Boltzmann equations
82C22 Interacting particle systems in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82D05 Statistical mechanics of gases
82B05 Classical equilibrium statistical mechanics (general)

Keywords:

linear Boltzmann equation; hard potential collisions; higher velocity moments; time-space evolutions; elastic collisions; non-elastic collisions; sphere collisions; linear solution; hydrodynamic limit
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References:

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