Calculus of Variations and Geometric Measure Theory

P. Cannarsa - P. Cardaliaguet - C. Sinestrari

On a differential model for growing sandpiles with non-regular sources

created by cannarsa on 24 Apr 2008


Submitted Paper

Inserted: 24 apr 2008

Year: 2008


We consider a variational model that describes the growth of a sandpile on a bounded table under the action of a vertical source. The possible equilibria of such a model solve a boundary value problem for a system of nonlinear partial differential equations that we analyse when the source term is merely integrable. In addition, we study the asymptotic behavior of the dynamical problem showing that the solution converges asymptotically to an equilibrium that we characterise explicitly.

Keywords: granular matter, asymptotic profile, uniqueness of solutions, distance function