The coagulation-fragmentation equation describes the concentration $f_i(t)$ of particles of size $i \in \nn / \{0\}$ at time $t\geq 0$, in a spatially homogeneous infinite system of particles subjected to coalescence and break-up. We show that when the rate of fragmentation is sufficiently stronger than that of coalescence, $(f_i(t))_{i \in \nn / \{0\}}$ tends to an unique equilibrium as $t$ tends to infinity. Although we suppose that the initial datum is sufficiently small, we do not assume a detailed balance (or reversibility) condition. The rate of convergence we obtain is furthermore exponential.
Publié le : 2004-07-05
Classification:
Coalescence,
Fragmentation,
Differential equations,
Equilibrium,
82C05,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00147612,
author = {Fournier, Nicolas and Mischler, St\'ephane},
title = {Exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without a balance condition},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00147612}
}
Fournier, Nicolas; Mischler, Stéphane. Exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without a balance condition. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00147612/