Discrete H -theorem for finite volume discretization of a nonlinear kinetic system: application to hypocoercivity
Abstract
In this article, we study the long-time behavior of a finite-volume discretization for a nonlinear kinetic reaction model involving two interacting species. Building upon the seminal work of Favre, Pirner, Schmeiser [ Arch. Ration. Mech. Anal. 247 (2023), no. 4] , we extend the discrete exponential convergence to equilibrium result established in Bessemoulin-Chatard, Laidin, Rey [ IMA J. Numer. Anal. 45 (2025), no. 4] , which was obtained in a perturbative framework using weighted L 2 estimates. The analysis applies to a broader class of exponentially decaying initial data, without requiring proximity to equilibrium, by exploiting the properties of the Boltzmann entropy. The proof relies on the propagation of the initial L ∞ bounds, derived from monotonicity properties of the scheme, allowing controlled linearizations within the nonlinear entropy estimates. Moreover, we show that the time-discrete dissipation inherent to the numerical scheme plays a crucial stabilizing role, providing control over the nonlinear terms.
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BibTeX
@article{bessemoulinchatard2026discrete,
title = {{Discrete H -theorem for finite volume discretization of a nonlinear kinetic system: application to hypocoercivity}},
author = {Marianne Bessemoulin-Chatard and Tino Laidin and Thomas Rey},
journal = {Comptes Rendus. Mathématique},
year = {2026},
month = oct,
doi = {10.5802/crmath.855},
url = {https://hal.science/hal-05848336v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Discrete H -theorem for finite volume discretization of a nonlinear kinetic system: application to hypocoercivity
AU - Marianne Bessemoulin-Chatard
AU - Tino Laidin
AU - Thomas Rey
PY - 2026
DA - 2026/10/06
JO - Comptes Rendus. Mathématique
DO - 10.5802/crmath.855
UR - https://hal.science/hal-05848336v1
AB - In this article, we study the long-time behavior of a finite-volume discretization for a nonlinear kinetic reaction model involving two interacting species. Building upon the seminal work of Favre, Pirner, Schmeiser [ Arch. Ration. Mech. Anal. 247 (2023), no. 4] , we extend the discrete exponential convergence to equilibrium result established in Bessemoulin-Chatard, Laidin, Rey [ IMA J. Numer. Anal. 45 (2025), no. 4] , which was obtained in a perturbative framework using weighted L 2 estimates. The analysis applies to a broader class of exponentially decaying initial data, without requiring proximity to equilibrium, by exploiting the properties of the Boltzmann entropy. The proof relies on the propagation of the initial L ∞ bounds, derived from monotonicity properties of the scheme, allowing controlled linearizations within the nonlinear entropy estimates. Moreover, we show that the time-discrete dissipation inherent to the numerical scheme plays a crucial stabilizing role, providing control over the nonlinear terms.
SN - 1631-073X
SN - 1778-3569
ER -