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

被引:2
|
作者
Favre, Gianluca [1 ]
Pirner, Marlies [2 ]
Schmeiser, Christian [1 ]
机构
[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
[2] Wurzburg Univ, Dept Math, Emil Fischer Str 40, D-97074 Wurzburg, Germany
基金
奥地利科学基金会;
关键词
KINETIC-MODELS; CHEMICAL-PROCESSES; EQUATIONS; CHEMOTAXIS;
D O I
10.1007/s00205-023-01902-8
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
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页数:15
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