A new solvable model of aggregation kinetics

A new reaction kernel, K(j, k) = 2-q(j)-q(k) with 0 < q < 1, is introduced, for which the Smoluchowski equations of aggregation (c)over dot(j) = 1/2 Sigma(k,l=1)(infinity) K(k, l)c(k)c(l)[delta(k+l,j)-delta(k,j)-delta(l,j)] can be solved. The time evolution of the concentrations c(j)(t) and of their moments M-n(t) = Sigma(j=1)(infinity) j(n)c(j)(t) is analysed. The c(j)(t) decay at large times as t(-(2-qj)) in striking contrast to the behaviour of the constant kernel K(j, k) = 2, for which c(j)(t) behaves as t(-2) at large times. On the other hand, the moments behave in leading order at large times exactly like the moments of the constant kernel, though differences appear at higher orders.