Browsing by Author "Rossi, Julio D."

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    Boundary fluxes for nonlocal diffusion
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi
    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. (c) 2006 Elsevier Inc. All rights reserved.
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    The blow-up problem for a semilinear parabolic equation with a potential
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.
    Let Omega be a bounded smooth domain in R-N. We consider the problem u(t) = Delta u + V(x)u(P) in Omega x [0, T), with Dirichlet boundary conditions u = 0 on partial derivative Omega x [0, T) and initial datum u (x, 0) = M phi (x) where M >= 0, phi 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 these estimates we find that, for M large, the blow-up set concentrates near the points where phi(P-1) V attains its maximum. (c) 2007 Elsevier Inc. All rights reserved.