Abstract
In this paper, we prove the global existence and uniqueness of the solutions to the initial-value problem for the coagulation–fragmentation equation with singular coagulation kernel and multiple fragmentation kernel. The solution obtained in this case also satisfies the mass conservation law. The proof is based on strong convergence methods applied to suitably chosen unbounded coagulation kernels having singularities in both the coordinate axes and satisfying certain growth conditions, which can possibly reach up to a quadratic growth at infinity, and the fragmentation kernel covers a very large class of unbounded functions.
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