Published Paper

Inserted: 25 jul 2003
Last Updated: 4 mar 2005

Journal: Convex Analysis
Volume: 12
Number: 1
Pages: 221-237
Year: 2005

Abstract:

\newcommand{\eps}{\varepsilon}

In this paper we study the homogenization of the linear equation $$ R(\eps^{-1}x){\partial u_\eps \over\partial t}- \textrm{div} (a(\eps^{-1}x) \nabla u_\eps) = f\ , $$ with appropriate initialfinal conditions, where $R$ is a measurable bounded periodic function and $a$ is a bounded uniformly elliptic matrix, whose coefficients $a_{ij}$ are measurable periodic functions. Since we admit that $R$ may vanish and change sign, the usual compactness of the solutions in $L^2$ may not hold if the mean value of $R$ is zero.

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