American Institute of Mathematical Sciences

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

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)). Citation: Aníbal Rodríguez-Bernal, Robert Willie. Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic problem. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 385-410. doi: 10.3934/dcdsb.2005.5.385  [1] Davide Guidetti. 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