Browsing by Author "Elgueta, Manuel"
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- ItemAn inhomogeneous nonlocal diffusion problem with unbounded steps(SPRINGER BASEL AG, 2016) Cortazar, Carmen; Elgueta, Manuel; Garcia Melian, Jorge; Martinez, SalomeWe consider the following nonlocal equation
- ItemAnalysis of an elliptic system with infinitely many solutions(2016) Cortázar, Carmen; Elgueta, Manuel; García Melián, Jorge
- ItemAsymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes(2012) Cortazar, Carmen; Elgueta, Manuel; Quiros, Fernando; Wolanski, NoemiThe paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, u (t) = J*u-u := Lu, in an exterior domain, Omega, which excludes one or several holes, and with zero Dirichlet data on . When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation.
- ItemAsymptotic behavior for a nonlocal diffusion equation in exterior domains : the critical two-dimensional case(2016) Cortázar, Carmen; Elgueta, Manuel; Quirós, F.; Wolanski, N.
- ItemASYMPTOTIC BEHAVIOR FOR A NONLOCAL DIFFUSION EQUATION ON THE HALF LINE(2015) Cortázar, Carmen; Elgueta, Manuel; Quiros, Fernando; Wolanski, Noemí
- ItemAsymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains(2016) Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi
- ItemBoundary fluxes for nonlocal diffusion(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2007) Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, NoemiWe 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.
- ItemEXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SOME INHOMOGENEOUS NONLOCAL DIFFUSION PROBLEMS(SIAM PUBLICATIONS, 2009) Cortazar, Carmen; Elgueta, Manuel; Garcia Melian, Jorge; Martinez, SalomeWe consider the nonlocal evolution Dirichlet problem u(t)(x, t) = f(Omega) J(x-y/g(y)) u(y, t)/g(y)(N) dy- u(x, t), x is an element of Omega, t > 0; u = 0, x is an element of R-N\Omega, t >= 0; u(x, 0) = u(0)(x), x is an element of R-N; where Omega is a bounded domain in R-N, J is a Holder continuous, nonnegative, compactly supported function with unit integral and g is an element of C((Omega) over bar) is assumed to be positive in Omega. We discuss existence, uniqueness, and asymptotic behavior of solutions as t -> |infinity. Moreover, we prove the existence of a positive stationary solution when the inequality g(x) <= delta(x) holds at every point of Omega, where delta(x) = dist(x, partial derivative Omega). The behavior of positive stationary solutions near the boundary is also analyzed.
- ItemFinite mass solutions for a non local in homogeneous dispersal equation(2015) Cortázar, Carmen; Elgueta, Manuel; García-Melián, Jorge; Martínez, Salomé
- ItemHow to approximate the heat equation with neumann boundary conditions by nonlocal diffusion problems(2008) Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, NoemiWe 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.
- ItemNonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions(2009) Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.We present a model for nonlocal diffusion with Dirichlet boundary conditions in a bounded smooth domain. We prove that solutions of properly rescaled nonlocal problems approximate uniformly the solution of the corresponding Dirichlet problem for the classical heat equation.
- ItemNonnegative solutions of semilinear elliptic equations in half-spaces(2016) Cortázar, Carmen; Elgueta, Manuel; Garcia, J.
- ItemStationary Sign Changing Solutions for an Inhomogeneous Nonlocal Problem(INDIANA UNIV MATH JOURNAL, 2011) Cortazar, Carmen; Elgueta, Manuel; Garcia Melian, Jorge; Martinez, SalomeWe consider the following nonlocal equation:
- ItemSymmetry of large solutions for semilinear elliptic equations in a ball(2019) Cortázar, Carmen; Elgueta, Manuel; Garcia-Melian, J.
- ItemThe 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.