Noureddine Igbida

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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. by studying the limit, as p → ∞, of the nonlocal p-Laplacian(More)
We study the asymptotic behavior of the sign-changing solution of the equation ut = ∇·(|u|−α∇u)+f, when the diffusion becomes very fast, i.e. as α ↑ 1. We prove that a solution uα(t) converges in L(Ω), uniformly for t in subsets with compact support in (0, T ), to a solution of ut = ∇·(|u|−1∇u)+f. In contrast with the case of α < 1, we prove that the(More)
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