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May  2005, 5(2): 385-410. doi: 10.3934/dcdsb.2005.5.385

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

Aníbal Rodríguez-Bernal 1, and  Robert Willie 2,

1. 

Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040
2. 

Universidad Complutense de Madrid, Facultad de Ciencias Matemática, Matemática Aplicada, 28040, Madrid, Spain

Received  December 2002 Revised  July 2004 Published  February 2005

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 $C(\overline{\Omega})$. In the parabolic case we prove convergence in the functional space $L^\infty ((0,T),L^2(\Omega)) \bigcap L^2 ((0,T),H^1(\Omega)).
Keywords: convergence of solutions., linear elliptic problem, eigenvalue problem, linear parabolic problem, non homogeneous boundary conditions, large diffusion, analytic semigroups.
Mathematics Subject Classification: 35Bxx,35B25, 35B40, 35B4.
Citation: Aníbal Rodríguez-Bernal, Robert Willie. Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic problem. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 385-410. doi: 10.3934/dcdsb.2005.5.385
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