Convergence to equilibria of solutions to the coagulation-fragmentation equations

Costa, Fernando Pestana da

http://hdl.handle.net/10400.2/6413

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Authors

Costa, Fernando Pestana da

Abstract(s)

The Coagulation-Fragmentation equations are a model for the dynamics of cluster growth and consist of a countable number of non-locally coupled ordinary differential equations, modelling the concentration of the various clusters. The framework for the study of these equations is to see them as a nonlinear ODE in an appropriate infinite dimensional Banach space. A number of results about existence, uniqueness, density conservation, and asymptotic behaviour of solutions have been obtained in recent years. In the present paper we review some of the more recent results on the asymptotic behaviour of solutions as time tends to infinity. We pay special attention to the different behaviour of solutions in the weak-star and in the strong topologies of the phase space. This distinction can be interpreted in terms of a dynamic phase transition in the physical system modelled by the equations. It is shown that a balance between the relative strength of coagulation and fragmentation is crucial for that distinct behaviour to take place.