Exact differential equations for diffusion limited aggregation

A central difficulty in many problems involving statistical dynamics of surfaces or lines is the preservation in model equations of the correct topological integrity. This paper continues a series by the authors which study problem, and contains equations for the evolution of surfaces by the deposition of particles out of an ensemble of diffusing particles onto the surface. It is shown that closed equations can be given to describe the process and that these equations honour the topological integrity of non-penetrating surfaces.