FAST SLOW DIFFUSION AND COLLAPSING SANDPILES

We regard the limit as p --> infinity of the flow governed by the p-la placian as providing a simplistic model for the ''collapse of an initi ally unstable sandpile.'' Upon rescaling to stretch out the initial la yer we obtain some simple dynamics and provide fairly explicit solutio ns in certain casts involving nonlocal geometric curvature motion. In particular we note that such models entail ''instantaneous'' mass tran sfer governed by Monge-Kantorovich theory. (C) 1997 Academic Press.