On a class of continuous coagulation-fragmentation equations
The simultaneous coagulation and fragmentation of systems of particle clusters is studied in this article. Each cluster is assumed to be fully described by a real number denoting its size. Effects such as multiple coagulation are ignored, assuming that the rates of the reactions only depend on the sizes of the clusters. The author proves the existence of solutions for product-type coagulation kernels with a weak fragmentation. The last two sections deal with the effects of gelation, i.e., the failure of density conservation. This is done both in the pure coagulation and in the coagulation-fragmentation case and estimates on \(\rho(t)\) and upper bounds (although not optimal) on the gelation time are obtained.
scientific article; zbMATH DE number 1545269
scientific article