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 solves a boundary value problem for a system of nonlinear partial differential equations that we analyze 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 characterize explicitly.
Cannarsa, P., Cardaliaguet, P., Sinestrari, C. (2009). On a differential model for growing sandpiles with non-regular sources. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 343, 656-675 [10.1080/03605300902909966].
On a differential model for growing sandpiles with non-regular sources
CANNARSA, PIERMARCO;SINESTRARI, CARLO
2009-01-01
Abstract
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 solves a boundary value problem for a system of nonlinear partial differential equations that we analyze 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 characterize explicitly.| File | Dimensione | Formato | |
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