Liapunov functionals for Smoluchowski's coagulation equation and convergence to self-similarity

An alternative proof of the convergence to self-similar profiles for solutions to the Smoluchowski coagulation equation with constant coagulation kernel is provided. In contrast to the previous approaches which rely on the Laplace transform, a dynamical systems approach is used on the equation written in self-similar variables, for which several Liapunov functionals are identified.