On a Differential Model for Sandpiles Growing in a Silo

2025/09/29 by Crasta, Graziano, Malusa, Annalisa
#35C15 #35F30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.24618

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.

Citations

• Duality theory and optimal transport for sand piles growing in a silos

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