BZ Seminar in Analysis: Juan J. L. Velázquez (University of Bonn)

Oscillatory behaviour in coagulation-fragmentation models

It is well known that in kinetic models satisfying the so-called detailed balance condition, it is possible to construct an entropy functional which can be used to derive convergence to equilibrium results. On the other hand, there are many physical situations (typically open systems) where it is natural to use kinetic equations for which the detailed balance condition fails. In these cases more complicated dynamical behaviours can arise, for instance oscillatory behaviours. A class of kinetic equations where it is not a priori obvious if temporal oscillations can take place are the coagulation-fragmentation equations. These equations have been extensively used to model chemical systems. In this talk I will describe two examples of coagulation-fragmentation models for which the onset of periodic oscillations can be rigorously proved. One of the models describes the formation of large clusters in a kinetic equation having a source of monomers. The second model is a closed coagulation-fragmentation model without external monomer sources, but in which the detailed balance condition fails at one of the reactions.

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