EDP-convergence for nonlinear fast-slow reaction systems with detailed balance*

被引:7
作者
Mielke, Alexander [1 ,2 ]
Peletier, Mark A. [3 ]
Stephan, Artur [1 ]
机构
[1] Weierstrass Inst Angew Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany
[2] Humboldt Univ, Inst Math, Unter Linden 6, D-10099 Berlin, Germany
[3] TU Eindhoven, Inst Complex Mol Syst, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
关键词
reaction system; mass-action kinetics; gradient structure; evolutionary gamma convergence; CHEMICAL-REACTIONS; THERMODYNAMICS;
D O I
10.1088/1361-6544/ac0a8a
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows. In general, the effective entropy will no longer be of Boltzmann type and the reactions will no longer satisfy mass-action kinetics.
引用
收藏
页码:5762 / 5798
页数:37
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