Hypocoercivity and reaction-diffusion limit for a nonlinear generation-recombination model
Analysis of PDEs
2023-08-07 v3
Abstract
A reaction-kinetic model for a two-species gas mixture undergoing pair generation and recombination reactions is considered on a flat torus. For dominant scattering with a non-moving constant-temperature background the macroscopic limit to a reaction-diffusion system is carried out. Exponential decay to equilibrium is proven for the kinetic model by hypocoercivity estimates. This seems to be the first rigorous derivation of a nonlinear reaction-diffusion system from a kinetic model as well as the first hypocoercivity result for a nonlinear kinetic problem without smallness assumptions. The analysis profits from uniform bounds of the solution in terms of the equilibrium velocity distribution.
Cite
@article{arxiv.2012.15622,
title = {Hypocoercivity and reaction-diffusion limit for a nonlinear generation-recombination model},
author = {Gianluca Favre and Marlies Pirner and Christian Schmeiser},
journal= {arXiv preprint arXiv:2012.15622},
year = {2023}
}