Convergence to Equilibrium for the Discrete Coagulation-Fragmentation Equations with Detailed Balance
Convergence to Equilibrium for the Discrete Coagulation-Fragmentation Equations with Detailed Balance
复制标题
具有详细平衡的离散凝固-破碎方程收敛到平衡点
DOI：
10.1007/s10955-007-9373-2
复制
发表时间：
2007
影响因子：
1.6
通讯作者：
J. Cañizo
中科院分区：
文献类型：
--
作者：
J. Cañizo
摘要
在详细的平衡和一些额外的限制的大小的系数的条件下，我们确定的平衡分布的离散凝聚-破碎方程组的解决方案收敛到大的时间，从而表明，有一个临界质量，标志着改变的行为的解决方案。这是以前已知的，只有在特殊情况下，作为广义贝克尔-杜林方程。我们的证明是基于熵和熵生产之间的不平等，这也给出了一些信息的收敛速度的平衡下的临界质量的解决方案。
Abstract
Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for large times, thus showing that there is a critical mass which marks a change in the behavior of the solutions. This was previously known only for particular cases as the generalized Becker–Döring equations. Our proof is based on an inequality between the entropy and the entropy production which also gives some information on the rate of convergence to equilibrium for solutions under the critical mass.