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We present a model for nonlocal diffusion with Dirichlet boundary conditions in a bounded smooth domain. We prove that solutions of properly re-scaled non local problems approximate uniformly the solution of the corresponding Dirichlet problem for the classical heat equation.

Let Ω be a bounded smooth domain in R . We consider the problem ut = ∆u + V (x)u in Ω × [0, T ), with Dirichlet boundary conditions u = 0 on ∂Ω × [0, T ) and initial datum u(x, 0) = Mu0(x) where M ≥ 0, u0 is positive and compatible with the boundary condition. We give estimates for the blow up time of solutions for large values of M . As a consequence of… (More)

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… (More)

R J(x − y)u(x, t)dy is the rate at which they are leaving location x to travel to all other sites. This consideration, in the absence of external sources, leads immediately to the fact that the density u satisfies equation (1.1). Throughout this note we shall assume also that J is a decreasing radial function whose support is the unit ball. Under these… (More)

- Carmen Cortázar, Manuel Elgueta, Jorge García-Melián, Salomé Martínez
- SIAM J. Math. Analysis
- 2009

- Michinori Ishiwata, Futoshi Takahashi, +4 authors Marta Garćıa-Huidobro
- 2015

- Carmen Cortázar, Manuel Elgueta, Fernando Quirós, Noemi Wolanski
- SIAM J. Math. Analysis
- 2016

- Carmen Cortazar, Salome Martinez, Carmen Cortázar, Manuel Elgueta, Jorge Garćıa-Melián
- 2015

In this paper we study the asymptotic behavior of the following nonlocal inhomogeneous dispersal equation ut(x, t) = ∫ R J ( x− y g(y) ) u(y, t) g(y) dy − u(x, t) x ∈ R, t > 0, where J is an even, smooth, probability density, and g, which accounts for a dispersal distance, is continuous and positive. We prove that if g(|y|) ∼ a|y| as |y| → ±∞ for some 0 < a… (More)

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