Representation of equilibrium solutions to the table problem of growing sandpiles
Cannarsa, Piermarco; Cardaliaguet, Pierre (2004), Representation of equilibrium solutions to the table problem of growing sandpiles, Interfaces and free boundaries, 6, 4, p. 435-464. http://dx.doi.org/10.4171/JEMS/16
TypeArticle accepté pour publication ou publié
Journal nameInterfaces and free boundaries
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Abstract (EN)In the dynamical theory of granular matter the so-called table problem consists instudying 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.
Subjects / KeywordsGranular matter; eikonal equation; singularities; semiconcave functions; viscosity solutions; optimal mass transfer
Showing items related by title and author.
Hölder regularity of the normal distance with an application to a PDE model for growing sandpiles. Cannarsa, Piermarco; Giorgieri, Elena; Cardaliaguet, Pierre (2007) Article accepté pour publication ou publié