Abstract. We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions.
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.
This article in devoted to the study of the nonlocal dispersal equationand its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on g and J , we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as t → ∞, showing that they converge locally to zero.
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