On the differential model of sandpiles growing in a silo

G. Crasta, A. Malusa

Sapienza Università di Roma, Roma, Italy

Abstract: We discuss some features of a boundary value problem for a system of PDEs that describes the growth of a sandpile in a container under the action of a vertical source. In particular, we characterize the long-term behavior of the profiles, and we provide a sufficient condition on the vertical source that guarantees the convergence to the equilibrium in a finite time. We show by counterexamples that a stable configuration may not be reached in a finite time, in general, even if the source is time-independent. Finally, we provide a complete characterization of the equilibrium profiles.

Keywords: system of partial differential equations, evolutionary problem, sandpile, surface profile, stationary solution, convergence in a finite time.

UDC: 517.9

DOI: 10.22363/2413-3639-2025-71-4-626-641