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