The authors study the existence, the uniqueness and a contraction property for solutions of the equation \[ -{\partial u(x,t)\over\partial t}= \int_{\mathbb{R}^N} J(x- y)|u(x,t)- u(y,t)|^{p-2} (u(x,t)- u(y,t))\,dy, \] where \((x,t)\in\Omega\times (0,T)\) and \(J\) is a compactly supported suitable function. The function \(u(x,t)\) is prescribed when \(x\in \mathbb{R}^N\setminus\Omega\).
Some convergence properties are studied. It is indicated that the case \(p\to\infty\) has applications to the formation of sandpiles.