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

(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.

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Bellieud, Michel. "Homogenization of evolution problems for a composite medium with very small and heavy inclusions." ESAIM: Control, Optimisation and Calculus of Variations 11.2 (2010): 266-284. <http://eudml.org/doc/90765>.

@article{Bellieud2010,
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. },
author = {Bellieud, Michel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Homogenization; memory effects; grain-like inclusions.; limit problem; grain-like inclusions},
language = {eng},
month = {3},
number = {2},
pages = {266-284},
publisher = {EDP Sciences},
title = {Homogenization of evolution problems for a composite medium with very small and heavy inclusions},
url = {http://eudml.org/doc/90765},
volume = {11},
year = {2010},
}

TY - JOUR
AU - Bellieud, Michel
TI - Homogenization of evolution problems for a composite medium with very small and heavy inclusions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 11
IS - 2
SP - 266
EP - 284
AB - 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.
LA - eng
KW - Homogenization; memory effects; grain-like inclusions.; limit problem; grain-like inclusions
UR - http://eudml.org/doc/90765
ER -

References

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