Related papers: Cauchy problem for the ellipsoidal BGK model for p…
We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for…
We consider networks for isentropic gas and prove existence of weak solutions for a large class of coupling conditions. First, we construct approximate solutions by a vector-valued BGK model with a kinetic coupling function. Introducing…
This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…
In [Phys. Rev. 94 (1954), 511-525], P.L. Bhatnagar, E.P. Gross and M. Krook introduced a kinetic equation (the BGK equation), effective in physical situations where the Knudsen number is small compared to the scales where Boltzmann's…
We develop a microscopic approach to the kinetic theory of many-particle systems with dissipative and potential interactions in presence of active fluctuations. The approach is based on a generalization of Bogolyubov--Peletminsky reduced…
We present a numerical method for simulating rarefied gases that interact with moving boundaries and rigid bodies. The gas is described by the BGK equation in Lagrangian form and solved using an Arbitrary Lagrangian-Eulerian method, in…
In this paper, the existence, uniqueness and regularity properties, Strichartz type estimates for solution of multipoint Cauchy problem for linear and nonlinear Schr\"odinger equations with general elliptic leading part is obtained.
Bhatnagar-Gross-Krook (BGK) equation is a relaxation model of the Boltzmann equation which is widely used in place of the Boltzmann equation for the simulation of various kinetic flow problems. In this work, we study the asymptotic…
A kinetic equation for the collisional evolution of stable, bound, self gravitating and slowly relaxing systems is established, which is valid when the number of constituents is very large. It accounts for the detailed dynamics and self…
We consider a Gross-Pitaevskii equation which appears as a model in the description of dipolar Bose-Einstein condensates, without a confining external trapping potential. We describe the asymptotic dynamics of solutions to the corresponding…
We study the existence and uniqueness of Lp-bounded mild solutions for a class ofsemilinear stochastic evolutions equations driven by a real L\'evy processes withoutGaussian component not square integrable for instance the stable process…
In this work, we propose a class of high order semi-Lagrangian scheme for a general consistent BGK model for inert gas mixtures. The proposed scheme not only fulfills indifferentiability principle, but also asymptotic preserving property,…
The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for marginal distribution functions, the dual BBGKY hierarchy for…
We study the global existence, uniqueness and exponential stability of mild solutions to the Boussinesq systems equipped with a generalized gravitational field on the framework of non-compact Riemannian manifolds. We work on some manifolds…
Simulating hypersonic flow around a space vehicle is challenging because of the multiscale and nonequilibrium nature inherent in these flows. To effectively deal with such flows, a novel particle particle hybrid scheme combining the…
In this paper, we investigate the Cauchy problem for both linear and semi-linear elliptic equations. In general, the equations have the form \[ \frac{\partial^{2}}{\partial…
The Vlasov-Maxwell-Boltzmann system is a fundamental model to describe the dynamics of dilute charged particles, where particles interact via collisions and through their self-consistent electromagnetic field. We prove the existence of…
A new model, inspired by the structure of galactic disks, for three-dimensional Bernstein-Greene-Kruskal (BGK) modes in a plasma with a uniform finite background magnetic field is presented. These modes are exact nonlinear solutions of the…
The model of inelastic Maxwell particles (IMP) allows one to derive some exact results which show the strong influence of inelasticity on the nonequilibrium properties of a granular gas. The aim of this work is to propose a simple model…
We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…