论文标题
具有详细平衡的非线性快速反应系统的EDP连接系统
EDP-convergence for nonlinear fast-slow reaction systems with detailed balance
论文作者
论文摘要
我们认为具有慢速和快速反应的质量行动动力学满足的非线性反应系统。众所周知，快速反应率极限可以由带有拉格朗日乘数的ODE和一组非线性约束，要求快速反应处于平衡状态。我们的目的是研究限制梯度结构，如果反应系统满足详细的平衡条件，则可以使用。 浓度向量上的梯度结构是根据相对玻尔兹曼熵和COSH型耗散电位给出的。我们表明，可以通过EDP收敛来严格地得出限制或有效的梯度结构，即从梯度流的能量散落原理的意义上进行收敛。通常，有效的熵将不再是Boltzmann类型，并且反应将不再满足质量动力学。
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.
