# Internal DLA and the Stefan problem

J. Gravner and J. Quastel

The {\it generalized internal diffusion limited aggregation (internal DLA)\/} is a stochastic growth model on a lattice in which the dynamics has two components. Firstly, particles execute a non--degenerate zero--range dynamics (for example, independent random walks) on sites which constitute the {\it occupied set\/}, that is, have occupancy number exceeding $\a$; furthermore, particles are stuck on sites with occupancy number at most $\a$. Secondly, a finite number of sites act as {\it sources\/} of particles. We prove that the hydrodynamic limit of generalized internal DLA is the one--phase Stefan problem and use this to study the asymptotic behavior of the occupied set.