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 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
- 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.