The diffusion approximation of the spatially homogeneous Boltzmann equation

DOI10.1215/S0012-7094-85-05201-9zbMath0612.60095MaRDI QIDQ1088312

Tadahisa Funaki

Publication date: 1985

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Boltzmann equationmartingale problemspatially homogeneous Landau equationstochastic spatially homogeneous caricature

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60)

Related Items (9)

Local existence, lower mass bounds, and a new continuation criterion for the Landau equation ⋮ Nonlinear master equation of multitype particle systems ⋮ The Enskog process ⋮ Distribution dependent SDEs for Landau type equations ⋮ Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials ⋮ Solutions of a class of nonlinear master equations ⋮ Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential ⋮ Measurability of optimal transportation and convergence rate for Landau type interacting particle systems ⋮ Uniqueness of bounded solutions for the homogeneous relativistic Landau equation with Coulomb interactions

Cites Work

• The diffusion approximation of the Boltzmann equation of Maxwellian molecules
• A certain class of diffusion processes associated with nonlinear parabolic equations
• [https://portal.mardi4nfdi.de/wiki/Publication:3347061 �quations de type de Boltzmann, spatialement homog�nes]
• [https://portal.mardi4nfdi.de/wiki/Publication:4043914 Diffusion processes associated with L�vy generators]
• Probabilistic treatment of the Boltzmann equation of Maxwellian molecules
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