The paper considers a simple model of radially symmetric cell which undergoes growth due to a continuous supply of nutrient, and disintegration as a result from the various tasks the cell performs. The boundary of the cell is a \free boundary", unknown in advance, which evolves by responding to both the growth and disintegration processes. If the nutrient concentration (at in nity) exceeds a ce...

Generalized internal diffusion limited aggregation is a stochastic growth model on the lattice in which a finite number of sites act as Poisson sources of particles which then perform symmetric random walks with an attractive zero-range interaction until they reach the first site which has been visited by fewer than α particles, at which point they stop. Sites on which particles are frozen cons...

In this paper we generalize the degenerate two{phase Stefan problem (Mullins{ Sekerka evolution) to multi{phase systems. We prove a conditional existence result for this evolution problem in the framework of geometric measure theory by using an implicit time discretization. In each time step we solve a variational problem for an energy functional that contains capillarity terms as well as bulk ...