Related papers: Boltzmann-type kinetic equations and discrete mode…
Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these…
The transport coefficients of a dilute gas of inelastic hard spheres immersed in a molecular gas are determined. We assume that the number density of the granular gas is much smaller than that of the surrounding molecular gas, so that the…
We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe-Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the…
This is a continuation of our series of works for the inhomogeneous Boltzmann equation. We study qualitative properties of classical solutions, precisely, the full regularization in all variables, uniqueness, non-negativity and convergence…
We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the initial datum is a nonnegative $L^2$ function, with bounded…
In this paper, we prove global in time existence, uniqueness and stability of mild solutions near vacuum for the 4-wave inhomogeneous kinetic wave equation, for Laplacian dispersion relation in dimension $d=2,3$. We also show that for…
We establish the hydrodynamic limit of the one-dimensional Boltzmann equation with hard-sphere collisions toward Riemann solutions of the compressible Euler system. The Riemann solutions covered by our result include generic superpositions…
Homogeneous Boltzmann-type equations are an established tool for modelling interacting multi-agent systems in sociophysics by means of the principles of statistical mechanics and kinetic theory. A customary implicit assumption is that…
This article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our…
The one-dimensional kinetic equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and frequency of collisions affine depending on the module of molecular velocity is constructed. Laws of preservation of number of…
N.N. Bogolyubov discovered that the Boltzmann-Enskog kinetic equation has microscopic solutions. They have the form of sums of delta-functions and correspond to trajectories of individual hard spheres. But the rigorous sense of the product…
A new type of kinetic models with non-instantaneous binary collisions is considered. Collisions are described by a transport process in the joint state space of a pair of particles. The interactions are of alignment type, where the states…
The note presents a classification of the relevant distinct types of solutions of the general Friedmann equation without assuming a priori restrictions for the parameters occurring in this equation. The emphasis is on the case of a…
The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…
We consider a general model of Hamiltonian wave systems with triple resonances, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. In this asymptotic limit we show that the correct…
This paper studies the quantum Boltzmann Nordheim equation from a Boltzmann equation for Haldane statistics. Strong solutions are obtained for the Cauchy problem with initial data in L1 and uniformly bounded on a one (resp. two or…
A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…
The kinetic theory of Maxwell and Boltzmann has been the subject of major scientific controversies. The alleged incompatibility between the reversible nature of the equations of classical mechanics and the increase of entropy, which, in the…
Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally…
A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…