Comptes Rendus
Nonlinear “double porosity” type model
[Un modèle non linéaire de type double porosité]
Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 435-440.

On étudie un problème variationnel inf uH 1 (Ω) Ω {a ϵ |u ϵ | m +g|u ϵ | m - mf ϵ u ϵ }dx dans un ouvert borné Ω= (ϵ) ¯ (ϵ) avec une microstructure (ϵ) non périodique ; aε=aε(x) vaut 1 dans (ϵ) et sup x (ϵ) a ϵ (x)0 lorsque ε→0. Un modèle homogénéisé est construit.

We consider a variational problem inf uH 1 (Ω) Ω {a ϵ |u ϵ | m +g|u ϵ | m - mf ϵ u ϵ }dx in a bounded domain Ω= (ϵ) ¯ (ϵ) with a microstructure (ϵ) which is not in general periodic; aε=aε(x) is of order 1 in (ϵ) and sup x (ϵ) a ϵ (x)0 as ε→0. A homogenized model is constructed.

Reçu le :
Révisé le :
Publié le :
DOI : 10.1016/S1631-073X(02)02269-0

Leonid Pankratov 1 ; Andrey Piatnitski 2, 3

1 Département de mathématiques, Institut des Basses Températures (FTINT), 47, av. Lénine, 61103, Kharkov, Ukraine
2 Narvik University College, HiN, 8505, Narvik, Norway
3 Lebedev Physical Institute RAS, 53, Leninski prospect, 117333, Moscow, Russia
@article{CRMATH_2002__334_5_435_0,
     author = {Leonid Pankratov and Andrey Piatnitski},
     title = {Nonlinear {\textquotedblleft}double porosity{\textquotedblright} type model},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {435--440},
     publisher = {Elsevier},
     volume = {334},
     number = {5},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02269-0},
     language = {en},
}
TY  - JOUR
AU  - Leonid Pankratov
AU  - Andrey Piatnitski
TI  - Nonlinear “double porosity” type model
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 435
EP  - 440
VL  - 334
IS  - 5
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02269-0
LA  - en
ID  - CRMATH_2002__334_5_435_0
ER  - 
%0 Journal Article
%A Leonid Pankratov
%A Andrey Piatnitski
%T Nonlinear “double porosity” type model
%J Comptes Rendus. Mathématique
%D 2002
%P 435-440
%V 334
%N 5
%I Elsevier
%R 10.1016/S1631-073X(02)02269-0
%G en
%F CRMATH_2002__334_5_435_0
Leonid Pankratov; Andrey Piatnitski. Nonlinear “double porosity” type model. Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 435-440. doi : 10.1016/S1631-073X(02)02269-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02269-0/

[1] E. Acerbi; V. Chiadò Piat; G. Dal Maso; D. Percivale An extension theorem from connected sets, and homogenization in general periodic domains, Nonlinear Anal., Volume 18 (1992), pp. 481-496

[2] T. Arbogast; J. Douglas; U. Hornung Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Appl. Math., Volume 21 (1990), pp. 823-826

[3] A. Bourgeat; M. Goncharenko; M. Panfilov; L. Pankratov A general double porosity model, C. R. Acad. Sci. Paris, Série IIb, Volume 327 (1999), pp. 1245-1250

[4] A. Bourgeat; A. Mikelic; A. Piatnitski Modèle de double porosité aléatoire, C. R. Acad. Sci. Paris, Série I, Volume 327 (1998), pp. 99-104

[5] A. Braides; A. Defranceschi Homogenization of Multiple Integrals, Oxford Lecture Ser. Math. Appl., 12, Clarendon Press, Oxford, 1998

[6] D. Cioranescu; J. Saint Jean Paulin Homogenization of Reticulated Structures, Appl. Math. Sci., 136, Springer-Verlag, New York, 1999

[7] Homogenization and Porous Media (U. Hornung, ed.), Interdisciplinary Appl. Math., 6, Springer-Verlag, New York, 1997

[8] E. Khruslov Asymptotic behavior of the solutions of the second boundary value problem in the case of the refinement of the boundary of the domain, Mat. Sb., Volume 106 (1978), pp. 604-621

[9] E. Khruslov Averaged models of diffusion in fractured–porous media, Dokl. Akad. Nauk SSSR, Volume 309 (1989), pp. 332-335 English translation in Soviet Phys. Dokl. 34 (1989) 980–981

[10] E. Khruslov; L. Pankratov Homogenization of boundary value problems for the Ginzburg–Landau equation in weakly connected domains (V. Marchenko, ed.), Spectral Theory and Related Topics, 19, American Mathematical Society, Providence, RI, 1994, pp. 233-268

[11] O. Ladyzhenskaya; N. Ural'tseva Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968

[12] L. Pankratov Homogenization of nonlinear Neumann elliptic and parabolic problems, Homogenization and Applications to Material Sciences, Math. Sci. Appl., 9, 1997, pp. 341-353

[13] A. Samarskii; V. Galaktionov; S. Kurdyumov; A. Mikhailov Blow-up in Quasilinear Parabolic Equations, De Gruyter, Berlin, 1995

[14] V. Zhikov; S. Kozlov; O. Oleinik Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, New York, 1994

Cité par Sources :

Commentaires - Politique