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Homogenization of evolution problems for a composite medium with very small and heavy inclusions

Published online by Cambridge University Press:  15 March 2005

Michel Bellieud
Michel Bellieud*
Affiliation:
Département de Mathématiques, Université de Perpignan, 52 av. de Villeneuve, 66100 Perpignan, France; bellieud@univ-perp.fr
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Abstract

We study the homogenization of parabolic or hyperbolic equations like \[ \rho_\varepsilon{\partial^n u_\varepsilon\over \partial t^n}- {\rm div}( a_\varepsilon\nabla u_\varepsilon) =f \ \ \hbox{ in } \quad {\O\times(0,T)}+ \ \ \hbox{\rm boundary conditions}, \quad n \in \{1,2\}, \] when the coefficients $\rho_\varepsilon$, $a_\varepsilon$ (defined in Ω) take possibly high values on a ε-periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.

Keywords

Homogenizationmemory effectsgrain-like inclusions.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 2 , April 2005 , pp. 266 - 284
Copyright
© EDP Sciences, SMAI, 2005

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References

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