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A Nonlocal coagulation-fragmentation model. (English) Zbl 0994.35054
Summary: 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 \({\varOmega}\). 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 \(L_1({\varOmega})\) setting. Our purpose is to study global (in time) existence, mass conservation and well-posedness of the model.

MSC:
35K57 Reaction-diffusion equations
92E20 Classical flows, reactions, etc. in chemistry
45K05 Integro-partial differential equations
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
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