ENTROPIC METHODS FOR THE STUDY OF THE LONG TIME BEHAVIOR OF KINETIC EQUATIONS

DOI10.1081/TT-100105366zbMath1038.82073OpenAlexW1990977691MaRDI QIDQ2780670

Cédric Villani, Laurent Desvillettes

Publication date: 2001

Published in: Transport Theory and Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/tt-100105366

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items

General entropy equations for structured population models and scattering, Entropy dissipation of Fokker-Planck equations on graphs, The method of differential contractions, Exponential decay for the fragmentation or cell-division equation, General relative entropy inequality: an illustration on growth models

Cites Work

• Unnamed Item
• Stability in \(L^ 1\) for the spatially homogeneous Boltzmann equation
• Global \(L^ p\)-properties for the spatially homogeneous Boltzmann equation
• The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
• Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation
• Entropy dissipation rate and convergence in kinetic equations
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds.
• Entropy production estimates for Boltzmann equations with physically realistic collision kernels
• A Maxwellian lower bound for solutions to the Boltzmann equation
• Logarithmic Sobolev Inequalities
• Stability and exponential convergence in Lp for the spatially homogeneous Boltzmann equation