Exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without a balance condition
Résumé
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.