Communications in Mathematical Sciences

Volume 20 (2022)

Number 3

Stability of measure solutions to a generalized Boltzmann equation with collisions of a random number of particles

Pages: 877 – 896

DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n3.a11

Authors

Henryk Gacki (Faculty of Science and Technology, University of Silesia, Katowice, Poland)

Łukasz Stettner (Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland)

Abstract

In the paper we study a measure version of the evolutionary nonlinear Boltzmann-type equation in which we admit a random number of collisions of particles. We consider first a stationary model and use two methods to find its fixed points: the first based on Zolotarev seminorm and the second on Kantorovich–Rubinstein maximum principle. Then a dynamic version of Boltzmann-type equation is considered and its asymptotic stability is shown.

Keywords

generalized Boltzmann equation, stability, collisions of particles, Zolotariev seminorm, Kantorovich–Rubinstein maximum principle

2010 Mathematics Subject Classification

35Q20, 82B21, 82B31

Full Text (PDF format)

Received 6 April 2020

Received revised 16 April 2021

Accepted 24 October 2021

Published 21 March 2022