Geodesic
A diffusion equation for composite materials
Electronic journal of differential equations, Tome 2000 (2000)
Zbl   EuDML
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 
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/
@article{EJDE_2000__2000__a140,
     author = {El Hajji,  Mohamed},
     title = {A diffusion equation for composite materials},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0936.35176},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a140/}
}
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