Coagulation, fragmentation and growth processes in a size structured population

An equation describing the dynamical behaviour of phytoplankton cells is considered in which the effects of cell division and aggregration are incorporated by coupling the coagulation-fragmentation equation with the McKendrick-von Foerster renewal model of an age-structured population. Under appropriate conditions on the model parameters, the associated initial-boundary value problem is shown to be well posed in a physically relevant Banach space.