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.
"Duality theory and optimal transport for sand piles growing in a silos." Adv. Differential Equations 20 (9/10) 859 - 886, September/October 2015.