Geodesic
A diffusion equation for composite materials
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we study the asymptotic behavior of solutions to the diffusion equation with non-homogeneous Neumann boundary conditions. This equation models a composite material that occupies a perforated domain, in ${\Bbb R}^N$, with small holes whose sizes are measured by a number $r_\varepsilon$. We examine the case when $r_\varepsilon \varepsilon^{N/(N-2)}$ with zero-average data around the holes, and the case when $\lim_{\varepsilon\to 0}{r_\varepsilon/\varepsilon}=0$ with nonzero-average data.
Classification : 31C40, 31C45, 60J50, 31C35, 31B35
Keywords: diffusion equation, composite material, asymptotic behavior, $H^{0}$-convergence 
@article{EJDE_2000__2000__a140,
     author = {El Hajji, Mohamed},
     title = {A diffusion equation for composite materials},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a140/}
}
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El Hajji, Mohamed. A diffusion equation for composite materials. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a140/