Global solutions to the discrete coagulation equations

The existence of global solutions to the discrete coagulation equations is investigated for a class of coagulation rates of the form alpha (i,j) = r(i)r(j) + alpha (i,j) with alpha (i,j)less than or equal to Kr(i)r(j). In particular, global solutions are shown to exist when the sequence (r(i)) increases linearly or superlinearly with respect to i. In this case also, the failure of density conservation (indicating the occurrence of the gelation phenomenon) is studied.