Learn More
The purpose of this paper is to study the limit in L 1 (Ω), as t → ∞, of solutions of initial-boundary-value problems of the form u t − ∆w = 0 and u ∈ β(w) in a bounded domain Ω with general boundary conditions ∂w ∂η + γ(w) 0. We prove that a solution stabilizes by converging as t → ∞ to a solution of the associated stationary problem. On the other hand,(More)
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)
  • 1