A Partial Integrodifferential Equation in Granular Matter and Its Connection with a Stochastic Model
Noureddine Igbida · SIAM Journal on Mathematical Analysis · 2012
Our aim is to introduce and study a new partial integrodifferential equation (PIDE) associated with the dynamics of some physical granular structure with arbitrary component sizes, like a sandpile or sea dyke. Our PIDE is closely related to the nonlocal evolution problem introduced in [F. Andreu et al., Calc. Var. Partial Differential Equations, 35 (2009), pp. 279--316] by studying the limit, as $p\to\infty$, of the nonlocal $p$-Laplacian equation. We also show the connection between our PIDE and the stochastic model introduced by Evans and Rezakhanlou in [L. C. Evans and F. Rezakhanlou, Comm. Math. Phys., 197 (1998), pp. 325--345.] for modeling the sandpile problem.