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Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic problem

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Rodríguez Bernal, Aníbal and Willie, Robert (2005) Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic problem. Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences, 5 (2). pp. 385-410. ISSN 1531-3492

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Official URL: http://www.aimsciences.org/journals/displayArticles.jsp?paperID=939




Abstract

We make precise the sense in which spatial homogenization to a constant function in space is attained in a linear parabolic problem when large diffusion in all parts of the domain is assumed. Also interaction between diffusion and boundary flux terms is considered. Our starting point is a detailed analysis of the large diffusion effects on the associated elliptic and eigenvalue problems. Here convergence is shown in the energy space H-1(Omega) and in the space of continuous functions C(Omega). In the parabolic case we prove convergence in the functional space L-infinity((0, T), L-2(Omega)) boolean AND L-2((0, T), H-1(Omega)).


Item Type:Article
Uncontrolled Keywords:Linear parabolic problem; Non homogeneous boundary conditions; Linear elliptic problem; Eigenvalue problem; Large diffusion; Analytic semigroups; Convergence of solutions; Nonlinear boundary-conditions; Attractors; Equations; Behavior; Systems
Subjects:Sciences > Mathematics > Functions
ID Code:17781
Deposited On:18 Jan 2013 09:07
Last Modified:12 Dec 2018 15:07

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