A semigroup approach to the convergence rate of a collisionless gas

DOI10.3934/krm.2020038zbMath1464.35277arXiv1911.03228OpenAlexW3082176541MaRDI QIDQ2224471

Armand Bernou

Publication date: 3 February 2021

Published in: Kinetic and Related Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.03228

zbMATH Keywords

transport equationsMaxwellian diffusion boundary conditionscollisionless gassubgeometric Harris' theorem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20) Initial-boundary value problems for linear first-order PDEs (35F16) Transport equations (35Q49)

Related Items (11)

On quantitative hypocoercivity estimates based on Harris-type theorems ⋮ Knudsen type group for time in ℝ and related Boltzmann type equations ⋮ Damping of Kinetic Transport Equation with Diffuse Boundary Condition ⋮ On eventual compactness of collisionless kinetic semigroups with velocities bounded away from zero ⋮ A coupling approach for the convergence to equilibrium for a collisionless gas ⋮ Convergence toward the steady state of a collisionless gas with Cercignani–Lampis boundary condition ⋮ Convergence rate to equilibrium for collisionless transport equations with diffuse boundary operators: a new tauberian approach ⋮ Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups ⋮ Exponential mixing of Vlasov equations under the effect of gravity and boundary ⋮ Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition ⋮ Existence of a nonequilibrium steady state for the nonlinear BGK equation on an interval

Cites Work

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• Hypocoercivity
• On The Trace Problem For Solutions Of The Vlasov Equation
• Relaxation of a free-molecular gas to equilibrium caused by interaction with Vessel wall
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