ABSTRACT
Existence and uniqueness of solutions to are obtained by first using semigroup-based techniques to deal with the linear fragmentation part of the equation, and then treating coagulation as a nonlinear perturbation. This chapter aims to prove the existence of weak solutions to the C-F equation and the starting point of the analysis is the well-posedness of the C-F equation with truncated kernels. It deals with an estimate of the contribution of the coagulation term to the growth of the moment of order m when the coagulation kernel grows algebraically. A common feature of the previous uniqueness results is that they only deal with coagulation and fragmentation coefficients for which the gelation phenomenon is not expected to occur.
