A global existence theorem for Smoluchowski’s coagulation equations

where the bij and Ck are continuous functions of t such that bij = bji > 0 and Ck > 0. The bij arising in applications typically increase without bound as i andj increase, so that (1) is beyond the reach of standard results on differential equations in Banach spaces. The case b,j 0) initial solution which does not, in general, extend to t > 1. The bij arising in most applications satisfy the more restrictive condition bij < i + j, for which case the present note demonstrates the existence of global, well-behaved solutions.