In this paper we study the homogenization of the linear equation $$ R(\eps^{-1}x){\partial u_\eps \over\partial t}- \textrm{div} (a(\eps^{-1}x) \cdot \nabla u_\eps) = f $$ 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.

Homogenization of changing-type evolution equations / Amar, Micol; Dall'Aglio, Andrea; F., Paronetto. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 12:(2005), pp. 221-237.

Homogenization of changing-type evolution equations

AMAR, Micol;DALL'AGLIO, Andrea;
2005

Abstract

In this paper we study the homogenization of the linear equation $$ R(\eps^{-1}x){\partial u_\eps \over\partial t}- \textrm{div} (a(\eps^{-1}x) \cdot \nabla u_\eps) = f $$ 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.
2005
Homogenization; evolution equations; compactness properties
01 Pubblicazione su rivista::01a Articolo in rivista
Homogenization of changing-type evolution equations / Amar, Micol; Dall'Aglio, Andrea; F., Paronetto. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 12:(2005), pp. 221-237.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/240319
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