Small eigenvalues of the low temperature linear relaxation Boltzmann equation with a confining potential

DOI10.1007/s00023-015-0410-4zbMath1343.35182arXiv1410.8738OpenAlexW2026015837MaRDI QIDQ270235

Virgile Robbe

Publication date: 7 April 2016

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.8738

zbMATH Keywords

relaxation to equilibriumresolvent estimatesspectral solutionhypocoercivityconfining potentialinhomogeneous kinetic equationslinear Boltzmann equationlow-lying eigenvalues (spectral gap)nonlocal collision termPT (parity-time) symmetrysemigroup decayspectral estimates

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Spectrum, resolvent (47A10) Eigenvalue problems for linear operators (47A75) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Irreversible thermodynamics, including Onsager-Machlup theory (82C35) Boltzmann equations (35Q20)

Related Items (3)

Hypocoercivity in metastable settings and kinetic simulated annealing ⋮ Metastability results for a class of linear Boltzmann equations ⋮ Low-lying eigenvalues and convergence to the equilibrium of some piecewise deterministic Markov processes generators in the small temperature regime

Cites Work

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• Spectral Theory and its Applications
• Hypocoercivity for linear kinetic equations conserving mass
• Semiclassical Analysis for the Kramers–Fokker–Planck Equation

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