Fragmentation Arising from a Distributional Initial Condition II

We consider a class of fragmentation equations in which the distribution of daughter particles formed when a parent particle fragments is governed by a homogeneous function. A systematic procedure is presented for constructing a space of distributions in which initial-value problems involving singular initial conditions can be analysed. This procedure makes use of results on sun dual semigroups and equicontinuous semigroups on locally convex spaces. Explicit solutions are obtained for the the case when the fragmentation processes are governed by power-law kernels and have monodisperse initial conditions modelled by Dirac delta distributions. Rigorous justification is thereby provided for results obtained more formally by Ziff and McGrady. AMS subject classifications: 47D06, 34G10, 45K05, 46F05. Abbreviated Title: Distributional Fragmentation.