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

Piermarco Cannarsa (1) , Pierre Cardaliaguet (2) , Carlo Sinestrari (1)

1 DIPMAT - Dipartimento di Matematica [Roma II]
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Optimisation et contrôle [math.OC]

Piermarco Cannarsa, Pierre Cardaliaguet, Carlo Sinestrari. On a differential model for growing sandpiles with non-regular sources. Communications in Partial Differential Equations, 2009, 34 (7-9), pp.656--675. ⟨hal-00657561⟩