ASYMPTOTIC-BEHAVIOR OF SOLUTIONS TO THE DIFFUSIVE FRAGMENTATION-COAGULATION SYSTEM

We study the time asymptotics of solutions to the diffusive fragmentat ion-coagulation system which we derived in a previous work [J.-F. Coll et, 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 en ergy dissipation rate of the system. In the case where no detailed bal ance equilibrium exists, we show the existence of an attractor by usin g classical energy inequalities and some estimates on higher moments o f the solution. (C) 1998 Elsevier Science B.V.