Nonlinear “double porosity” type model

Leonid Pankratov; Andrey Piatnitski

doi:10.1016/S1631-073X(02)02269-0

Nonlinear “double porosity” type model
[Un modèle non linéaire de type double porosité]

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

Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 435-440.

Résumé
Abstract

On étudie un problème variationnel $\inf_{u \in H^{1} (Ω)} \int_{Ω} {a^{ϵ} | \nabla u^{ϵ} |^{m} + g | u^{ϵ} |^{m} - {mf}^{ϵ} u^{ϵ}} d x$ dans un ouvert borné $Ω = ℱ^{(ϵ)} \cup {\bar{ℳ}}^{(ϵ)}$ avec une microstructure $ℱ^{(ϵ)}$ non périodique ; a^ε=a^ε(x) vaut 1 dans $ℱ^{(ϵ)}$ et $\sup_{x \in ℳ^{(ϵ)}} a^{ϵ} (x) \to 0$ lorsque ε→0. Un modèle homogénéisé est construit.

We consider a variational problem $\inf_{u \in H^{1} (Ω)} \int_{Ω} {a^{ϵ} | \nabla u^{ϵ} |^{m} + g | u^{ϵ} |^{m} - {mf}^{ϵ} u^{ϵ}} d x$ in a bounded domain $Ω = ℱ^{(ϵ)} \cup {\bar{ℳ}}^{(ϵ)}$ with a microstructure $ℱ^{(ϵ)}$ which is not in general periodic; a^ε=a^ε(x) is of order 1 in $ℱ^{(ϵ)}$ and $\sup_{x \in ℳ^{(ϵ)}} a^{ϵ} (x) \to 0$ as ε→0. A homogenized model is constructed.

Reçu le : 2001-09-13
Révisé le : 2002-01-08
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02269-0

Affiliations des auteurs :

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

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     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},
}

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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/

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