2024/08/19 by Marianne Bessemoulin‐Chatard, Tino Laidin, Thomas Rey · 1 voice
Physics and Astronomy · Mathematics · #Advanced Thermodynamics and Statistical Mechanics #Mathematical Biology Tumor Growth #Gas Dynamics and Kinetic Theory
paper · doi:10.1093/imanum/drae058
openalex created_date 2024/03/09 · openalex publication_date 2024/08/19 · openalex updated_date 2026/08/01
Abstract In this article we propose a finite-volume discretization of a one-dimensional nonlinear reaction kinetic model proposed in Neumann & Schmeiser (2016), which describes a two-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 L2 hypocoercivity method introduced in Dolbeault et al. (2015). From this we can deduce a local result for the discrete nonlinear problem, in the sense that small initial perturbations from the steady state are considered. As in the continuous framework this result requires the establishment of a maximum principle, which necessitates the use of monotone numerical fluxes.