On Linear Hypocoercive BGK Models

DOI10.1007/978-3-319-32144-8_1zbMath1353.35113arXiv1510.02290OpenAlexW4300368388MaRDI QIDQ2832847

Anton Arnold, Eric Anders Carlen, Franz Achleitner

Publication date: 15 November 2016

Published in: From Particle Systems to Partial Differential Equations III (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.02290

zbMATH Keywords

entropy methodkinetic equationshypocoercivitydiscrete and continuous phase spacesexponential rates of relaxation

Mathematics Subject Classification ID

Linear first-order PDEs (35F05)

Related Items

Hypocoercivity with Schur complements, Large time convergence of the non-homogeneous Goldstein-Taylor equation, Time averages for kinetic Fokker-Planck equations, Hypocoercivity and controllability in linear semi‐dissipative Hamiltonian ordinary differential equations and differential‐algebraic equations, Hypocoercivity without confinement, The hypocoercivity index for the short time behavior of linear time-invariant ODE systems, On multi-dimensional hypocoercive BGK models, A note on Fisher information hypocoercive decay for the linear Boltzmann equation, φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations, Hypocoercivity for a BGK model for gas mixtures, Hypocoercivity of piecewise deterministic Markov process-Monte Carlo, Uniqueness of the non-equilibrium steady state for a 1d BGK model in kinetic theory, Sharp decay estimates in local sensitivity analysis for evolution equations with uncertainties: from ODEs to linear kinetic equations, Sharpening of decay rates in Fourier based hypocoercivity methods, Hypocoercivity in Phi-Entropy for the Linear Relaxation Boltzmann Equation on the Torus

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The BGK model with external confining potential: existence, long-time behaviour and time-periodic Maxwellian equilibria
• Modified logarithmic Sobolev inequalities in discrete settings
• Global existence to the BGK model of Boltzmann equation
• Hypocoercivity for kinetic equations with linear relaxation terms
• Weighted \(L^ \infty\) bounds and uniqueness for the Boltzmann BGK model
• Non-negative matrices and Markov chains.
• Stability of dynamical systems. On the role of monotonic and non-monotonic Lyapunov functions
• Logarithmic Sobolev inequalities for finite Markov chains
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• Large-time behavior in non-symmetric Fokker-Planck equations
• Markov Chains
• Hypocoercivity for linear kinetic equations conserving mass
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
• New Approach to Nonequilibrium Processes