Recent Advances in the Theory of Kinetic Equations of Many Colliding Particles

Authors

  • V.I. Gerasimenko Institute of Mathematics of the NAS of Ukraine, 3, Tereshchenkivs’ka Str., 01004, Kyiv, Ukraine.
  • I.V. Gapyak Department of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 2, Academician Glushkov Av., 03187, Kyiv, Ukraine.

DOI:

https://doi.org/10.9734/bpi/mcsru/v2/4175

Keywords:

BBGKY hierarchy, dual Boltzmann hierarchy, Boltzmann kinetic equation, Boltzmann–Grad scaling limit, hard sphere collisions

Abstract

The chapter presents a novel perspective on kinetic equations for systems of many colliding particles, which are governed by a hierarchy of fundamental evolution equations for observables at the microscopic scale. For this purpose, the Boltzmann–Grad asymptotics of the non-perturbative solution to the Cauchy problem for a hierarchy of evolution equations for reduced observables of such systems is constructed. As a result, based on the collective behavior of colliding particles of observables the generalization of the Boltzmann kinetic equation is derived, and the process of propagation of initial correlations is described.

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Published

2025-01-25

How to Cite

V.I. Gerasimenko, & I.V. Gapyak. (2025). Recent Advances in the Theory of Kinetic Equations of Many Colliding Particles. Mathematics and Computer Science: Research Updates Vol. 2, 142–163. https://doi.org/10.9734/bpi/mcsru/v2/4175

Issue

Mathematics and Computer Science: Research Updates Vol. 2

Section

Chapters