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 / De Pascale L.; Jimenez C.. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 20:9-10(2015), pp. 859-886.
Duality Theory and Optimal transport for sand piles growing in a silos.
DE PASCALE, LUIGI;
2015
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.
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