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)−τ ψτ (y/s(t)) for (t, y) ∈ (0, T )×(0,∞), where T is some arbitrary positive real number, s(t) = ((3−τ)(T − t))−1/(3−τ) and the parameter τ ranges in a given interval [τc, 3). In addition, the second moment of these self-similar solutions blows up at time T . As for the profile ψτ , it belongs to L1(0,∞; y2dy) for each τ ∈ [τc, 3) but its behaviour for small and large y varies with the parameter τ . MSC 2000: 45J05, 34C11