Homogenization of evolution problems for a composite medium with very small and heavy inclusions
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 11, Issue: 2, page 266-284
- ISSN: 1292-8119
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topBellieud, 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
top- M. Bellieud, Homogenization of evolution problems in a fiber reinforced structure. J. Convex Anal.11 (2004) 363–385.
- M. Bellieud and G. Bouchitté, Homogenization of elliptic problems in a fiber reinforced structure. Non local effects. Ann. Scuola Norm. Sup. Cl. Sci. IV26 (1998) 407–436.
- M. Bellieud and I. Gruais, Homogénéisation d'une structure élastique renforcée de fibres très rigides. Effets non locaux. C. R. Math., Problèmes mathématiques de la mécanique337 (2003) 493–498.
- M. Bellieud and I. Gruais, Homogenization of an elastic material reinforced by very stiff or heavy fibers. Non local effects. Memory effects. J. Math. Pures Appl.84 (2005) 55–96.
- H. Brezis, Analyse fonctionnelle. Masson, Paris (1983).
- G. Dal Maso, An introduction to -Convergence. Progress Nonlinear Differential Equations Appl., Birkhäuser, Boston (1993).
- E.Y. Khruslov, Homogenized models of composite media. Progress Nonlinear Differential Equations Appl., Birkhäuser (1991).
- J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Dunod, Paris 1 (1968).
- U. Mosco, Composite media and asymptotic Dirichlet forms. J. Funct. Anal.123 (1994) 368–421.
- G. Panasenko, Multicomponent homogenization of the vibration problem for incompressible media with heavy and rigid inclusions. C. R. Acad. Sci. Paris I321 (1995) 1109–1114.
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