Geometric analysis of the linear Boltzmann equation. I: Trend to equilibrium

DOI10.1007/s40818-015-0003-zzbMath1398.35142arXiv1401.8227OpenAlexW1789036918MaRDI QIDQ1661375

Daniel Han-Kwan, Matthieu Léautaud

Publication date: 16 August 2018

Published in: Annals of PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.8227

zbMATH Keywords

control theorykinetic theorylarge time behaviourhypocoercivitylinear Boltzmann equationgeometric control conditions

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Asymptotic behavior of solutions to PDEs (35B40) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Transport processes in time-dependent statistical mechanics (82C70) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20)

Related Items (14)

On quantitative hypocoercivity estimates based on Harris-type theorems ⋮ Hypocoercivity with Schur complements ⋮ Control to Flocking of the Kinetic Cucker--Smale Model ⋮ On uniform observability of gradient flows in the vanishing viscosity limit ⋮ A model of particles interacting with thermal traps ⋮ Hypocoercivity without confinement ⋮ Trajectorial hypocoercivity and application to control theory ⋮ Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition ⋮ Quantitative rates of convergence to equilibrium for the degenerate linear Boltzmann equation on the torus ⋮ Mathematical and numerical study of a dusty Knudsen gas mixture ⋮ A note on Fisher information hypocoercive decay for the linear Boltzmann equation ⋮ Existence of invariant densities and time asymptotics of conservative linear kinetic equations on the torus without spectral gaps ⋮ Hypocoercivity of piecewise deterministic Markov process-Monte Carlo ⋮ Trend to equilibrium and spectral localization properties for the linear Boltzmann equation

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