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On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations. (English) Zbl 0912.45011

Author’s summary: The paper deals with the spatially homogeneous Boltzmann equation when grazing collisions are involved. We study in a unified setting the Boltzmann equation without cut-off, the Fokker-Planck-Landau equation, and the asymptotics of grazing collisions for a very broad class of potentials; in particular, we are able to derive rigorously the Landau equation for the Coulomb potential. In order to do so, we introduce a new definition of weak solutions, based on entropy production.
Reviewer: V.Yurko (Saratov)

MSC:

45K05 Integro-partial differential equations
45M05 Asymptotics of solutions to integral equations
82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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