On two continuous models for the dynamics of sandpile surfaces

We consider a modified BCRE model for pile surface dynamics (Bouchaud, Cates, Ravi Prakash, and Edwards, J. Phys. I France, v. 4, p. 1383, 1994) and show that in the long-scale limit this model converges to a quasistationary model of pile growth in the form of an evolutionary variational inequality (Prigozhin, Phys. Rev. E, v. 49, p. 1161, 1994).