From the discrete to the continuous coagulation-fragmentation equations

Author： Laurençot Philippe   Mischler Stéphane  

Publisher： Royal Society of Edinburgh

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.132, Iss.5, 2002-10, pp. : 1219-1248

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Abstract

The connection between the discrete and the continuous coagulation-fragmentation models is investigated. A weak stability principle relying on a priori estimates and weak compactness in L1 is developed for the continuous model. We approximate the continuous model by a sequence of discrete models and, writing the discrete models as modified continuous ones, we prove the convergence of the latter towards the former with the help of the above-mentioned stability principle. Another application of this stability principle is the convergence of an explicit time and size discretization of the continuous coagulation-fragmentation model.

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