Long time behavior of discrete velocity kinetic equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915428908924928 |
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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 |