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Fragmentation-diffusion model. Existence of solutions and their asymptotic behaviour. (English) Zbl 0912.35031
The discrete fragmentation-diffusion infinite system is studied. It describes dynamics of clusters degradation in the framework of discrete coagulation-fragmentation models. The fields of applications are polymer science, atmosphere physics and colloidal chemistry. The authors consider only mass-preserving (MPS) solutions. Existence of MPS is proved, and MPS are constructed as the limit of solutions of finite systems approximating the original one. Well-posedness for MPS is obtained. The long-time behaviour of MPS is investigated, and asymptotic convergence to spatially homogeneous equilibrium states is obtained.

35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
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