Probabilistic interpretation and numerical approximation of a Kac equation without cutoff

DOI10.1016/S0304-4149(99)00056-3zbMath1009.76081OpenAlexW2077363599WikidataQ127097182 ScholiaQ127097182MaRDI QIDQ1613657

Laurent Desvillettes, Carl Graham, Sylvie Méléard

Publication date: 29 August 2002

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(99)00056-3

zbMATH Keywords

stochastic differential equationrate of convergencenumerical approximationunique solutionstochastic particle systemsprobabilistic interpretationnoncutoff Kac equationnonlinear pure-jump Markov process

Mathematics Subject Classification ID

Stochastic analysis applied to problems in fluid mechanics (76M35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (22)

Strict positivity of the density for simple jump processes using the tools of support theorems. Application to the Kac equation without cutoff ⋮ A pure jump Markov process associated with Smoluchowski's coagulation equation ⋮ Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules ⋮ Quantitative propagation of chaos for generalized Kac particle systems ⋮ Kac's process with hard potentials and a moderate angular singularity ⋮ THE BOUNDED CONFIDENCE MODEL OF OPINION DYNAMICS ⋮ Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas ⋮ Uniqueness for a class of spatially homogeneous Boltzmann equations without angular cutoff ⋮ Global Solution for the Spatially Inhomogeneous Non-cutoff Kac Equation ⋮ Explicit decay rate for the Gini index in the repeated averaging model ⋮ Construction of Boltzmann and McKean-Vlasov type flows (the sewing lemma approach) ⋮ Solving Landau equation for some soft potentials through a probabilistic approach. ⋮ On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity ⋮ A toy-model study of the grazing collisions in the kinetic theory ⋮ Brownian approximation and Monte Carlo simulation of the non-cutoff Kac equation ⋮ Asymptotic of grazing collisions and particle approximation for the Kac equation without Cutoff ⋮ Probability Approaches to Spatially Homogeneous Boltzmann Equations ⋮ A stochastic particle numerical method for 3D Boltzmann equations without cutoff ⋮ Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit ⋮ Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications ⋮ Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The theory of the nonlinear Boltzmann equation for Maxwell molecules in Fourier representation
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• The mathematical theory of dilute gases
• Chaos hypothesis for a system interacting through shared resources
• Stochastic particle approximations for generalized Boltzmann models and convergence estimates
• Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas
• Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit
• About the regularizing properties of the non-cut-off Kac equation
• [https://portal.mardi4nfdi.de/wiki/Publication:3347061 �quations de type de Boltzmann, spatialement homog�nes]
• Local solutions in gevrey classes to the nonlinear Boltzmann equation without cutoff
• Central limit theorem for a system of Markovian particles with mean field interactions
• A Convergence Proof for Nanbu’s Simulation Method for the Full Boltzmann Equation
• Probabilistic treatment of the Boltzmann equation of Maxwellian molecules
• Une définition des solutions renormalisées pour l'équation de Boltzmann sans troncature angulaire
• Stochastic approximations of the solution of a full Boltzmann equation with small initial data

This page was built for publication: Probabilistic interpretation and numerical approximation of a Kac equation without cutoff