Homogenization of evolution problems for a composite medium with very small and heavy inclusions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 266-284.

We study the homogenization of parabolic or hyperbolic equations like

ρ ε n u ε t n - div (a ε u ε )=finΩ×(0,T)+boundaryconditions,n{1,2},
when the coefficients ρ ε , a ε (defined in Ø) take possibly high values on a ε-periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.

DOI : 10.1051/cocv:2005007
Classification : 35K05, 35L05, 73B27
Mots clés : homogenization, memory effects, grain-like inclusions
@article{COCV_2005__11_2_266_0,
     author = {Bellieud, Michel},
     title = {Homogenization of evolution problems for a composite medium with very small and heavy inclusions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {266--284},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {2},
     year = {2005},
     doi = {10.1051/cocv:2005007},
     mrnumber = {2141890},
     zbl = {1091.35011},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv:2005007/}
}
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
PY  - 2005
SP  - 266
EP  - 284
VL  - 11
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2005007/
DO  - 10.1051/cocv:2005007
LA  - en
ID  - COCV_2005__11_2_266_0
ER  - 
%0 Journal Article
%A Bellieud, Michel
%T Homogenization of evolution problems for a composite medium with very small and heavy inclusions
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2005
%P 266-284
%V 11
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv:2005007/
%R 10.1051/cocv:2005007
%G en
%F COCV_2005__11_2_266_0
Bellieud, Michel. Homogenization of evolution problems for a composite medium with very small and heavy inclusions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 266-284. doi : 10.1051/cocv:2005007. http://www.numdam.org/articles/10.1051/cocv:2005007/

[1] M. Bellieud, Homogenization of evolution problems in a fiber reinforced structure. J. Convex Anal. 11 (2004) 363-385. | Zbl

[2] M. Bellieud and G. Bouchitté, Homogenization of elliptic problems in a fiber reinforced structure. Non local effects. Ann. Scuola Norm. Sup. Cl. Sci. IV 26 (1998) 407-436. | Numdam | Zbl

[3] 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 mécanique 337 (2003) 493-498. | Zbl

[4] 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. | Zbl

[5] H. Brezis, Analyse fonctionnelle. Masson, Paris (1983). | MR | Zbl

[6] G. Dal Maso, An introduction to Γ-Convergence. Progress Nonlinear Differential Equations Appl., Birkhäuser, Boston (1993). | MR | Zbl

[7] E.Y. Khruslov, Homogenized models of composite media. Progress Nonlinear Differential Equations Appl., Birkhäuser (1991). | MR | Zbl

[8] J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Dunod, Paris 1 (1968). | Zbl

[9] U. Mosco, Composite media and asymptotic Dirichlet forms. J. Funct. Anal. 123 (1994) 368-421. | Zbl

[10] G. Panasenko, Multicomponent homogenization of the vibration problem for incompressible media with heavy and rigid inclusions. C. R. Acad. Sci. Paris I 321 (1995) 1109-1114. | Zbl

Cité par Sources :