Résumé en anglais

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.