A nonlocal coagulation-fragmentation model

Volume 27 / 2000

Mirosław Lachowicz, Dariusz Wrzosek Applicationes Mathematicae 27 (2000), 45-66 DOI: 10.4064/am-27-1-45-66


A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local models the analysis can be carried out in the $L_1(Ω)$ setting. Our purpose is to study global (in time) existence, mass conservation and well-posedness of the model.


  • Mirosław Lachowicz
  • Dariusz Wrzosek

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