Discrete hypocoercivity for a nonlinear kinetic reaction model
<|reference_start|>Discrete hypocoercivity for a nonlinear kinetic reaction model: 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.<|reference_end|>
@article{bessemoulin-chatard2024discrete,
    title={Discrete hypocoercivity for a nonlinear kinetic reaction model},
    author={Marianne Bessemoulin-Chatard and Tino Laidin and Thomas Rey},
    journal={arXiv preprint arXiv:2403.04699},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.04699},
    primaryClass={math.NA cs.NA}
}