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

TL;DR

This paper establishes existence and uniqueness results for a PDE system modeling sandpile growth in silos, utilizing duality theory in optimal transport and discrete source approximations.

Contribution

It introduces a novel approach combining duality in optimal transport with discrete source approximation to analyze sandpile growth PDEs.

Findings

Proved existence of solutions for the PDE system.

Proved uniqueness of solutions for the PDE system.

Applied duality theory to model sandpile growth.

Abstract

We prove existence and uniqueness of solutions for a system of PDEs which describes the growth of a sandpile in a silos with flat bottom under the action of a vertical, measure source. The tools we use are a discrete approximation of the source and the duality theory for optimal transport (or Monge-Kantorovich) problems.