Regularity and long time behavior of the Boltzmann equation for granular gases

DOI10.1016/j.jmaa.2005.12.044zbMath1104.35008OpenAlexW2070817840MaRDI QIDQ855669

Xian-Wen Zhang

Publication date: 7 December 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.12.044

zbMATH Keywords

dissipative collisionspseudo-Maxwellian approximation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05)

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Strong convergence towards homogeneous cooling states for dissipative Maxwell models

Cites Work

• On the Boltzmann equation for diffusively excited granular media
• Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas
• A non-Maxwellian steady distribution for one-dimensional granular media
• Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation.
• Moment equations for a granular material in a thermal bath
• Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas
• Nonlinear kinetic equations with dissipative collisions
• On some properties of kinetic and hydrodynamic equations for inelastic interactions.
• Contractive metrics for a Boltzmann equation for granular gases: Diffusive equilibria
• Shear flow of a granular material
• On diffusive equilibria in generalized kinetic theory.