Search results for "82C05"

showing 2 items of 2 documents

On the propagation of a perturbation in an anharmonic system

2007

We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.

Thermal equilibriumPhysicsAnharmonicityTime evolutionAnharmonic crystals; Propagation velocity; Statistical and Nonlinear Physics; Mathematical PhysicsPerturbation (astronomy)FOS: Physical sciencesStatistical and Nonlinear Physicsanharmonic crystals; propagation velocityMathematical Physics (math-ph)Upper and lower bounds82C05 82D20Classical mechanicsPropagation velocityAnharmonic crystalsSettore MAT/07 - Fisica MatematicaMathematical Physics
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Empirical measures and Vlasov hierarchies

2013

The present note reviews some aspects of the mean field limit for Vlasov type equations with Lipschitz continuous interaction kernel. We discuss in particular the connection between the approach involving the N-particle empirical measure and the formulation based on the BBGKY hierarchy. This leads to a more direct proof of the quantitative estimates on the propagation of chaos obtained on a more general class of interacting systems in [S.Mischler, C. Mouhot, B. Wennberg, arXiv:1101.4727]. Our main result is a stability estimate on the BBGKY hierarchy uniform in the number of particles, which implies a stability estimate in the sense of the Monge-Kantorovich distance with exponent 1 on the i…

MSC 82C05 (35F25 28A33)[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]FOS: Physical sciences01 natural sciencesVlasov type equation Mean-field limit Empirical measure BBGKY hierarchy Monge-Kantorovich distanceMathematics - Analysis of PDEs[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]FOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Applied mathematicsMonge-Kantorovich distanceDirect proof0101 mathematicsEmpirical measureMathematical PhysicsMean field limitMathematicsNumerical AnalysisHierarchy010102 general mathematicsVlasov type equationMathematical Physics (math-ph)Empirical measureBBGKY hierarchyLipschitz continuity010101 applied mathematicsKernel (algebra)Uniqueness theorem for Poisson's equationBBGKY hierarchyModeling and SimulationExponent82C05 (35F25 28A33)Analysis of PDEs (math.AP)Kinetic & Related Models
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