Recent Advances in the Theory of Kinetic Equations of Many Colliding Particles | Chapter 11 | Mathematics and Computer Science: Research Updates Vol. 2

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.

 

Author (s) Details

 

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.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v2/4175