Integral representation of the linear Boltzmann operator for granular gas dynamics with applications

DOI10.1007/s10955-007-9402-1zbMath1131.82040arXivmath/0701933OpenAlexW2079165161MaRDI QIDQ2468262

Luisa Arlotti, Bertrand Lods

Publication date: 22 January 2008

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701933

zbMATH Keywords

spectral theorylinear Boltzmann equationdetailed balance lawgranular gas dynamics

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Statistical mechanics of gases (82D05)

Related Items

New generation theorems in transport theory ⋮ Derivation of a non-autonomous linear Boltzmann equation from a heterogeneous Rayleigh gas ⋮ The derivation of the linear Boltzmann equation from a Rayleigh gas particle model ⋮ On perturbed substochastic semigroups in abstract state spaces ⋮ Equilibrium solution to the inelastic Boltzmann equation driven by a particle bath ⋮ Spectral analysis of transport equations with bounce-back boundary conditions ⋮ Inelastic Boltzmann equation driven by a particle thermal bath ⋮ Kinetic description of a Rayleigh gas with annihilation ⋮ Entropy dissipation estimates for the linear Boltzmann operator

Cites Work

• Unnamed Item
• Unnamed Item
• A perturbation theorem for positive contraction semigroups on \(L^ 1\)-spaces with applications to transport equations and Kolmogorov's differential equations
• The dissipative linear Boltzmann equation for hard spheres
• Mathematics of granular materials
• Cooling process for inelastic Boltzmann equations for hard spheres. II: Self-similar solutions and tail behavior
• Substochastic semigroups for transport equations with conservative boundary conditions
• Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
• Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models
• Stochastic operators, information, and entropy
• The mathematical theory of dilute gases
• The dissipative linear Boltzmann equation.
• Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails
• Dissipative hydrodynamic models for the diffusion of impurities in a gas
• Kinetic Theory for Binary Granular Mixtures at Low Density
• Modelling and numerical methods for the dynamics of impurities in a gas
• On substochastic C₀-semigroups and their generators
• Existence, uniqueness and properties of the solutions of the Boltzmann kinetic equation for a weakly ionized gas. I.
• Runaway Phenomena and Fluid Approximation Under High Fields in Semiconductor Kinetic Theory
• Kinetic Theory of Granular Gases
• On Solutions to the Linear Boltzmann Equation for Granular Gases