Fast/slow diffusion and growing sandpiles

We study a coupled system of ODE (introduced by the first author in SIAM J. Appl. Math. 22 (1972) 437-458) for the heights of growing, interacting sand cones. We show that these ODE correspond to the evolution in L(2) generated by the sub-differential of the convex Functional which vanishes on functions whose gradient has length less than or equal to one and is infinity otherwise. Additionally we explain how the ODE arise from evolutions governed by the p-Laplacian in the ''infinitely fast/infinitely slow'' diffusion limit as p --> infinity. (C) 1996 Academic Press, Inc.