The mass-conserving solutions of Smoluchowski's coagulation equation: The general bilinear kernel

Summary It is proved that for the general bilinear kernel with arbitrary initial conditions, the solutions to the discrete coagulation equation can exhibit one of the following types of behaviour: conservation of mass for all time, conservation of mass for a finite time only, or instantaneous gelation.Research supported in part by grants from Natural Sciences and Engineering Research Council of Canada.