Work

Discrete H -theorem for finite volume discretization of a nonlinear kinetic system: application to hypocoercivity

Year: 2026

Type: article

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.

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.855

Authors: Marianne Bessemoulin-Chatard, Tino Laidin, Thomas Rey