Geodesic
Homogenization in the problems of nonlinear diffusion
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 52-64 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of diffusion and slow convection of admixtures in the absolutely rigid porous medium is considered. The Stokes equations for the compressible viscous fluid which occupies the porous space and convective diffusion equation are the base equations. Viscous of fluid is depends on the concentration of admixture. Numerical simulations on a such model are unrealistic due to the fact that its main differential equations involve non-smooth oscillatory coefficients, both big and small, under the differentiation operators. The rigorous justification is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic. As the results, we derive the nonlinear system consisting of Darcy's equations of filtration, where viscous of fluid depends on the concentration of admixture, and homogenized convective diffusion equation.
Keywords: homogenization, nonlinear diffusion
Mots-clés : compressible viscous fluid. 
@article{SEMR_2010_7_a4,
     author = {S. A. Gritsenko},
     title = {Homogenization in the problems of nonlinear diffusion},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {52--64},
     year = {2010},
     volume = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a4/}
}
TY  - JOUR
AU  - S. A. Gritsenko
TI  - Homogenization in the problems of nonlinear diffusion
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2010
SP  - 52
EP  - 64
VL  - 7
UR  - http://geodesic.mathdoc.fr/item/SEMR_2010_7_a4/
LA  - ru
ID  - SEMR_2010_7_a4
ER  - 
%0 Journal Article
%A S. A. Gritsenko
%T Homogenization in the problems of nonlinear diffusion
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2010
%P 52-64
%V 7
%U http://geodesic.mathdoc.fr/item/SEMR_2010_7_a4/
%G ru
%F SEMR_2010_7_a4
S. A. Gritsenko. Homogenization in the problems of nonlinear diffusion. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 52-64. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a4/

[1] G. Nguetseng, “A general convergence result for a functional related to the theory of homogenization”, SIAM J. Math. Anal., 20 (1989), 608–623 | DOI | MR | Zbl

[2] A. M. Meirmanov, “Metod dvukhmasshtabnoi skhodimosti Nguetsenga v zadachakh filtratsii i seismoakustiki v uprugikh poristykh sredakh”, Sibirskii matematicheskii zhurnal, 48:3 (2007), 645–667 | MR | Zbl

[3] S. A. Gritsenko, R. N. Zimin, “Ob odnoi vspomogatelnoi zadache nelineinoi diffuzii v slaboszhimaemoi vyazkoi zhidkosti”, Nauchnye vedomosti BelGU, seriya fizika matematika (to appear)

[4] Zh.-L. Lions, Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972, 588 pp. | MR

[5] S. A. Gritsenko, “O diffuzii i medlennoi konvektsii primesi v slaboszhimaemoi vyazkoi zhidkosti”, Izvestiya Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 9:2 (2009), 19–24