Discrete hypocoercivity for a nonlinear kinetic reaction model

Marianne Bessemoulin-Chatard; Tino Laidin; Thomas Rey

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arXiv · 2403.04699

Discrete hypocoercivity for a nonlinear kinetic reaction model

Marianne Bessemoulin-Chatard·Tino Laidin·Thomas Rey

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Abstract

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.

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Marianne Bessemoulin-Chatard, Tino Laidin, Thomas Rey. 2024-03-07. Discrete hypocoercivity for a nonlinear kinetic reaction model. https://arxiv.org/abs/2403.04699

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