Long time behavior of discrete velocity kinetic equations

Fuente: arXiv
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Main Author: Toshpulatov, Gayrat
Format: Preprint
Published: 2025
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author Toshpulatov, Gayrat
author_facet Toshpulatov, Gayrat
contents We study long time behavior of some nonlinear discrete velocity kinetic equations in the one and three dimensions with periodic boundary conditions. We prove the exponential time decay of solutions towards the global equilibrium in the $L^2$ space. Our result holds for a wide class of interaction rates including the Goldstein-Taylor and Carleman equations, and the estimates on the rate of convergence are explicit and constructive. The technique is based on the construction of suitable Lyapunov functionals by modifying Boltzmann's entropy.
format Preprint
id arxiv_https___arxiv_org_abs_2508_03646
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Long time behavior of discrete velocity kinetic equations
Toshpulatov, Gayrat
Analysis of PDEs
35Q82, 35B40, 82C40
We study long time behavior of some nonlinear discrete velocity kinetic equations in the one and three dimensions with periodic boundary conditions. We prove the exponential time decay of solutions towards the global equilibrium in the $L^2$ space. Our result holds for a wide class of interaction rates including the Goldstein-Taylor and Carleman equations, and the estimates on the rate of convergence are explicit and constructive. The technique is based on the construction of suitable Lyapunov functionals by modifying Boltzmann's entropy.
title Long time behavior of discrete velocity kinetic equations
topic Analysis of PDEs
35Q82, 35B40, 82C40
url https://arxiv.org/abs/2508.03646