[HTML][HTML] Non-perturbative solutions of hierarchies of evolution equations for colliding particles
V Gerasimenko, I Gapyak - AIP Advances, 2024 - pubs.aip.org
The article deals with the challenge of the construction of solutions to hierarchies of
fundamental evolution equations for many colliding particles. The method of cluster …
fundamental evolution equations for many colliding particles. The method of cluster …
Advances in theory of evolution equations of many colliding particles
VI Gerasimenko, IV Gapyak - arXiv preprint arXiv:2308.04143, 2023 - arxiv.org
The review presents rigorous results of the theory of fundamental equations of evolution of
many-particle systems with collisions and also considers their connection with nonlinear …
many-particle systems with collisions and also considers their connection with nonlinear …
A system of stochastic differential equations modeling the Euler and the Navier-Stokes hydrodynamic equations
M Lachowicz - Japan journal of industrial and applied mathematics, 1993 - Springer
A system of stochastic differential equations modeling the Euler and the Navier-Stokes
hydrodynamic equations Page 1 Japan J. Indust. Appl. Math., 10 (1993), 109-131 A System of …
hydrodynamic equations Page 1 Japan J. Indust. Appl. Math., 10 (1993), 109-131 A System of …
Stochastic dynamics and Boltzmann hierarchy. I
DY Petrina, KD Petrina - Ukrainian Mathematical Journal, 1998 - Springer
Stochastic dynamics corresponding to the Boltzmann hierarchy is constructed. The Liouville-
Itô equations are obtained, from which we derive the Boltzmann hierarchy regarded as an …
Itô equations are obtained, from which we derive the Boltzmann hierarchy regarded as an …
Досягнення в теорії рівнянь еволюції багатьох частинок із зіткненнями
В Герасименко, І Гап'як - Збірник Праць Інституту математики …, 2023 - trim.imath.kiev.ua
Анотація В огляді подано строгі результати теорії фундаментальних еволюційних
рівнянь систем багатьох частинок із зіткненнями, а також розглянуто їх зв'язок із …
рівнянь систем багатьох частинок із зіткненнями, а також розглянуто їх зв'язок із …
On the Boltzmann-Grad Limit for the classical hard-spheres system
M Tessarotto - arXiv preprint arXiv:0806.4891, 2008 - arxiv.org
Despite the progress achieved by kinetic theory, the search of possible exact kinetic
equations remains elusive to date. This concerns, specifically, the issue of the validity of the …
equations remains elusive to date. This concerns, specifically, the issue of the validity of the …
Stochastic differential equations for the kinetic and hydrodynamic equations
M Lachowicz - Nonlinear Dynamics, 1994 - Springer
A finite system of stochastic interacting particles is considered. The system approximates the
solutions of the kinetic equations (the Boltzmann equation, the Boltzmann-Enskog equation) …
solutions of the kinetic equations (the Boltzmann equation, the Boltzmann-Enskog equation) …
Stochastic dynamics and Boltzmann hierarchy. III
DY Petrina, KD Petrina - Ukrainian Mathematical Journal, 1998 - Springer
Stochastic dynamics corresponding to the Boltzmann hierarchy is constructed. The Liouville-
Itô equations are obtained, from which we derive the Boltzmann hierarchy regarded as an …
Itô equations are obtained, from which we derive the Boltzmann hierarchy regarded as an …
Solutions of Bogolyubov equations for one-dimensional system of hard spheres
VI Gerasimenko - Theoretical and Mathematical Physics, 1992 - Springer
Solutions of Bogolyubov equations for one-dimensional system of hard spheres Page 1
SOLUTIONS OF BOGOLYUBOV EQUATIONS FOR ONE-DIMENSIONAL SYSTEM OF HARD …
SOLUTIONS OF BOGOLYUBOV EQUATIONS FOR ONE-DIMENSIONAL SYSTEM OF HARD …
Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble
DY Petrina, ED Petrina - Ukrainian Mathematical Journal, 1997 - Springer
We study equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit (d→ 0,
1/v→∞(z→∞), and d 3 (1/v)= const (d 3 z= const)). For this purpose, we use the Kirkwood …
1/v→∞(z→∞), and d 3 (1/v)= const (d 3 z= const)). For this purpose, we use the Kirkwood …