Advances in Differential Equations

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

Luigi De Pascale and Chloé Jimenez

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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.

Article information

Source
Adv. Differential Equations Volume 20, Number 9/10 (2015), 859-886.

Dates
First available in Project Euclid: 23 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1435064516

Mathematical Reviews number (MathSciNet)
MR3360394

Zentralblatt MATH identifier
1323.49031

Subjects
Primary: 49Q20: Variational problems in a geometric measure-theoretic setting 35K20: Initial-boundary value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40] 49K30: Optimal solutions belonging to restricted classes 35B99: None of the above, but in this section

Citation

De Pascale, Luigi; Jimenez, Chloé. Duality theory and optimal transport for sand piles growing in a silos. Adv. Differential Equations 20 (2015), no. 9/10, 859--886. https://projecteuclid.org/euclid.ade/1435064516.


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