Asymptotic behaviour of solutions to the diffusive fragmentationdashcoagulation system

We study the time asymptotics of solutions to the diffusive fragmentationdashcoagulation system which we derived in a previous work [J.-F. Collet, F. Poupaud, Transp. Theory and Stat. Phys. 25 (3–5) (1996) 503–513]. In the case where a detailed balance equilibrium exists, we derive convergence to such a state by using a careful analysis of the free energy dissipation rate of the system. In the case where no detailed balance equilibrium exists, we show the existence of an attractor by using classical energy inequalities and some estimates on higher moments of the solution.