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Displaying 41 – 60 of 109

Hypoelliptic estimates for some linear diffusive kinetic equations

Frédéric Hérau (2010)

Journées Équations aux dérivées partielles

This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations,...

Il sesto problema di Hilbert e le moderne teorie cinetiche.

Mario Pulvirenti (2004)

Bollettino dell'Unione Matematica Italiana

In questo contributo si discute qualche problema connesso alla derivazione delle equazioni cinetiche a partire dalla meccanica dei sistemi di particelle.

Interface cinétique / fluide : Un modèle simplifié

Alexis Vasseur (2002/2003)

Séminaire Équations aux dérivées partielles

Kac’s chaos and Kac’s program

Stéphane Mischler (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in [33] which gives a possible answer to some questions formulated by Kac in [25]. We also present some related recent results about Kac’s chaos and Kac’s program obtained in [34, 23, 13] by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.

Kinetic approach to systems of conservation laws

Benoît Perthame (1992)

Journées équations aux dérivées partielles

Kinetic equations with Maxwell boundary conditions

Stéphane Mischler (2010)

Annales scientifiques de l'École Normale Supérieure

We prove global stability results of DiPerna-Lionsrenormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which includes the so-called Maxwell boundary conditions, and we prove that it is realized (it is not only a boundary inequality condition as it has been established in previous works). We are able to deal with Boltzmann,...

Kinetic formulation for heterogeneous scalar conservation laws

Anne-Laure Dalibard (2006)

Annales de l'I.H.P. Analyse non linéaire

$L^{1}$ solutions to the stationary Boltzmann equation in a slab

Leif Arkeryd, Anne Nouri (2000)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Limites hydrodynamiques de l'équation de Boltzmann

Cédric Villani (2000/2001)

Séminaire Bourbaki

Low-variance direct Monte Carlo simulations using importance weights

Husain A. Al-Mohssen, Nicolas G. Hadjiconstantinou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present an efficient approach for reducing the statistical uncertainty associated with direct Monte Carlo simulations of the Boltzmann equation. As with previous variance-reduction approaches, the resulting relative statistical uncertainty in hydrodynamic quantities (statistical uncertainty normalized by the characteristic value of quantity of interest) is small and independent of the magnitude of the deviation from equilibrium, making the simulation of arbitrarily small deviations from equilibrium possible....

Many–Body Aspects of Approach to Equilibrium

Eric Carlen, M.C. Carvalho, Michael Loss (2000/2001)

Séminaire Équations aux dérivées partielles

Mean-field evolution of fermionic systems

Marcello Porta (2014/2015)

Séminaire Laurent Schwartz — EDP et applications

We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent...

Modelli matematici per la diffusione e il trasporto di particelle cariche

Simona Mancini (2000)

Bollettino dell'Unione Matematica Italiana

Nonresonant smoothing for coupled wave + transport equations and the Vlasov-Maxwell system.

François Bouchut, François Golse, Christophe Pallard (2004)

Revista Matemática Iberoamericana

On $2 \times 2$ systems of conservation laws with fluxes that are entropies.

Junk, Michael (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

On a variant of Korn’s inequality arising in statistical mechanics

L. Desvillettes, Cédric Villani (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We state and prove a Korn-like inequality for a vector field in a bounded open set of $ℝ^{N}$ , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case are...

On a variant of Korn's inequality arising in statistical mechanics

L. Desvillettes, Cédric Villani (2010)

ESAIM: Control, Optimisation and Calculus of Variations

On bilinear kinetic equations. Between micro and macro descriptions of biological populations

Mirosław Lachowicz (2003)

Banach Center Publications

In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including...

On conservative and entropic discrete axisymmetric Fokker-Planck operators

Emmanuel Frénod, Brigitte Lucquin-Desreux (1998)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

On global solutions for the Vlasov-Poisson system.

Zhidkov, Peter (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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