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Article Contents

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

• 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)).
Mathematics Subject Classification: 35Bxx,35B25, 35B40, 35B45.

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