Manuel Elgueta

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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)
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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