On the relation between rates of relaxation and convergence of wild sums for solutions of the Kac equation
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Publication:1776890
DOI10.1016/j.jfa.2004.06.011zbMath1108.82036OpenAlexW2066671493MaRDI QIDQ1776890
Eric Anders Carlen, Maria Conception Carvalho, Ester Gabetta
Publication date: 12 May 2005
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2004.06.011
Combinatorial probability (60C05) 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 (15)
Central limit theorem for the solution of the Kac equation ⋮ Central limit theorems for solutions of the Kac equation: speed of approach to equilibrium in weak metrics ⋮ On the global existence for the Kac model with external force ⋮ Some new results for McKean's graphs with applications to Kac's equation ⋮ Proof of a McKean conjecture on the rate of convergence of Boltzmann-equation solutions ⋮ On the rate of explosion for infinite energy solutions of the spatially homogeneous Boltzmann equation ⋮ Probabilistic view of explosion in an inelastic Kac model ⋮ Asymptotic of grazing collisions and particle approximation for the Kac equation without Cutoff ⋮ The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation ⋮ On the Depth of the Trees in the Mckean Representation of Wild's Sums ⋮ Probabilistic Investigations on the Explosion of Solutions of the KAC Equation with Infinite Energy Initial Distribution ⋮ Reaching the best possible rate of convergence to equilibrium for solutions of Kac's equation via central limit theorem ⋮ A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff ⋮ On the self-similar asymptotics for generalized nonlinear kinetic Maxwell models ⋮ Characterization of weak convergence of probability-valued solutions of general one-dimensional kinetic equations
Cites Work
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- Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
- Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range
- On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
- Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas
- On Boltzmann equations and Fokker-Planck asymptotics: Influence of grazing collisions
- On the optimal choice of coefficients in a truncated wild sum and approximate solutions for the Kac equation
- Fast and slow convergence to equilibrium for Maxwellian molecules via wild sums
- Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation.
- About the regularizing properties of the non-cut-off Kac equation
- Averaging lemmas without time Fourier transform and application to discretized kinetic equations
- Central limit theorem for Maxwellian molecules and truncation of the wild expansion
- On the spatially homogeneous landau equation for hard potentials part i : existence, uniqueness and smoothness
- An exponential formula for solving Boltzmann's equation for a Maxwellian gas
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