Work

Hypocoercivity and Reaction-Diffusion Limit for a Nonlinear Generation-Recombination Model

Year: 2023

Type: article

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.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-023-01902-8

Authors: Gianluca Favre, Marlies Pirner, Christian Schmeiser

Institutions: University of Vienna, University of Würzburg

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,790

Funders: Alexander von Humboldt-Stiftung, Austrian Science Fund, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni