Self-similar solutions to a coagulation equation with multiplicative kernel

Existence of self-similar solutions to the Oort-Hulst-Safronov coagulation equation with multiplicative coagulation kernel is established. These solutions are given by s(t)(-tau) psi(tau)(y/s(t)) for (t, y) is an element of (0, T) x (0, infinity), where T is some arbitrary positive real number, s(t) = ((3 - tau)(T - t))(-1/(3-tau)) and the parameter tau ranges in a given interval [tau(c), 3). In addition, the second moment of these self-similar solutions blows up at time T. As for the profile psi(tau), it belongs to L-1(0, infinity; y(2)dy) for each tau is an element of [tau(c), 3) but its behaviour for small and large y varies with the parameter tau. (c) 2006 Elsevier B.V. All rights reserved.