*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 initial*final 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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