Representation of equilibrium solutions to the table problem for growing sandpiles

54Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain Ω ⊂ ℝ2. The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge-Kantorovich problem, is the object of this paper. Our main result is an integral representation formula for the solution, in terms of the boundary curvature and of the normal distance to the cut locus of Ω.

References Powered by Scopus

Differential equations methods for the Monge-Kantorovich mass transfer problem

305Citations
N/AReaders
Get full text

Fast/slow diffusion and growing sandpiles

96Citations
N/AReaders
Get full text

Variational model of sandpile growth

95Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Multi-phase structural optimization via a level set method

119Citations
N/AReaders
Get full text

Shape and topology optimization

76Citations
N/AReaders
Get full text

Geometric constraints for shape and topology optimization in architectural design

61Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Cannarsa, P., & Cardaliaguet, P. (2004). Representation of equilibrium solutions to the table problem for growing sandpiles. Journal of the European Mathematical Society, 6(4), 435–464. https://doi.org/10.4171/JEMS/16

Readers' Seniority

Tooltip

Professor / Associate Prof. 2

50%

PhD / Post grad / Masters / Doc 2

50%

Readers' Discipline

Tooltip

Mathematics 2

67%

Engineering 1

33%

Save time finding and organizing research with Mendeley

Sign up for free