Discrete hypocoercivity for a nonlinear kinetic reaction model
| Autor: | Bessemoulin-Chatard, Marianne, Laidin, Tino, Rey, Thomas |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this article, we propose a finite volume discretization of a one dimensional nonlinear reaction kinetic model proposed in [Neumann, Schmeiser, Kint. Rel. Mod. 2016], which describes a 2-species recombination-generation process. Specifically, we establish the long-time convergence of approximate solutions towards equilibrium, at exponential rate. The study is based on an adaptation for a discretization of the linearized problem of the $L^2$ hypocoercivity method introduced in [Dolbeault, Mouhot, Schmeiser, 2015]. From this, we can deduce a local result for the discrete nonlinear problem. As in the continuous framework, this result requires the establishment of a maximum principle, which necessitates the use of monotone numerical fluxes. Comment: 30 pages, 8 figures |
| Databáze: | arXiv |
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