2020/12/31 by Gianluca Favre, Marlies Pirner, Christian Schmeiser · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth
paper · pdf · doi:10.1007/s00205-023-01902-8
openalex created_date 2021/07/19 · openalex publication_date 2023/07/31 · openalex updated_date 2026/08/01
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.