ABSTRACT
This chapter explores situations where an infringement of the physically expected property of mass conservation arises due to the existence of solutions that display mass loss. It shows that the finiteness of a moment of the initial condition of order higher than one is necessary to exclude instantaneous gelation. The chapter argues that instantaneous gelation and gelation after a finite time may occur simultaneously for a given kernel and depends on the integrability properties of the initial condition for large sizes. It provides an alternative proof of the occurrence of shattering which is in the same vein as those for gelation, as it relies on moment estimates combined with a technique that was developed in to prove that gelation takes place for the coagulation equation.
