Fast/slow diffusion and growing sandpiles (Q1817012)

This paper is mainly devoted to evolutions governed by the \(p\)-Laplacian: \[ (1)\quad u_{p,t}-\Delta_p u=f\text{ in }\mathbb{R}^n\times(0,\infty), \qquad (2)\quad u_p=g\text{ on }\mathbb{R}^n\times\{t=0\}, \] where \(\Delta_p u=\text{div}(|Du|^{p-2}Du)\). One proves that \(\lim_{p\to\infty}u_p=u\) by passing to the limit in (1)+(2). The limit equation is interpreted as a mathematical model for growing sandpiles.