Probabilistic Investigations on the Explosion of Solutions of the KAC Equation with Infinite Energy Initial Distribution

DOI10.1239/jap/1208358954zbMath1142.60013OpenAlexW2031749546MaRDI QIDQ5459911

Ester Gabetta, Eugenio Regazzini, Eric Anders Carlen

Publication date: 30 April 2008

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jap/1208358954

zbMATH Keywords

Boltzmann equationcentral limit theoremKac equation

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items

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 ⋮ Mean-field games and swarms dynamics in Gaussian and non-Gaussian environments ⋮ Multi-dimensional smoothing transformations: existence, regularity and stability of fixed points ⋮ Complete characterization of convergence to equilibrium for an inelastic Kac model ⋮ 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 ⋮ Central limit theorem for a class of one-dimensional kinetic equations ⋮ Reaching the best possible rate of convergence to equilibrium for solutions of Kac's equation via central limit theorem ⋮ Characterization of weak convergence of probability-valued solutions of general one-dimensional kinetic equations

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