Advances in theory of evolution equations of many colliding particles

TL;DR

This paper reviews rigorous mathematical results on the evolution equations governing many-particle systems with collisions and explores their link to nonlinear kinetic equations, highlighting advances in the theoretical understanding of particle dynamics.

Contribution

It provides a comprehensive overview of recent rigorous results in the theory of evolution equations for colliding particles and their connection to nonlinear kinetic models.

Findings

Rigorous results on evolution equations for many-particle systems

Connections established between collision-based equations and nonlinear kinetic equations

Highlights of mathematical advances in particle dynamics theory

Abstract

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 kinetic equations describing the collective behavior of particles in scaling approximations. This work is dedicated to the 160th anniversary of the birth of Dmytro Oleksandrovych Grave, the first academician of the Ukraine Academy of Sciences in mathematics and the founder of the Institute of Mathematics in 1920.