Journal of Convex Analysis 12 (2005), No. 1, 221--237
Copyright Heldermann Verlag 2005
Homogenization of Changing-Type Evolution Equations
Micol Amar
Dip. di Metodi e Modelli Matematici, Universita di Roma "La Sapienza", Via A. Scarpa 16,
00161 Roma, Italy
amar@dmmm.uniroma1.it
Andrea Dall'Aglio
Dip. di Metodi e Modelli Matematici, Universita di Roma "La Sapienza", Via A. Scarpa 16,
00161 Roma, Italy
aglio@dmmm.uniroma1.it
Fabio Paronetto
Dip. di Matematica "Ennio De Georgi", Università di Lecce, Via per Arnesano, 73100 Lecce, Italy
fabio.paronetto@unile.it
[Abstract-pdf]
\newcommand{\eps}{\varepsilon} We study the homogenization of the linear equation $$ R(\eps^{-1}x){\partial u_\eps \over\partial t}- \textrm{div} (a(\eps^{-1}x) \cdot \nabla u_\eps) = f\ , $$ 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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