Diffusion equation for composite materials

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 ${mathbb R}^N$, with small holes whose sizes are measured by a number $r_varepsil...

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Main Author:	Mohamed El Hajji
Format:	Article
Language:	English
Published:	Texas State University 2000-02-01
Series:	Electronic Journal of Differential Equations
Subjects:	Diffusion equation composite material asymptotic behavior $H^0$-convergence.
Online Access:	http://ejde.math.txstate.edu/Volumes/2000/15/abstr.html

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spelling	doaj-e3e81af60b644bb088fb30e5bc34ba222020-11-24T22:51:53ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912000-02-01200015111Diffusion equation for composite materialsMohamed El HajjiIn 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 ${mathbb R}^N$, 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 $lim_{varepsilono 0}{r_varepsilon/varepsilon}=0$ with nonzero-average data. http://ejde.math.txstate.edu/Volumes/2000/15/abstr.htmlDiffusion equationcomposite materialasymptotic behavior$H^0$-convergence.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mohamed El Hajji
spellingShingle	Mohamed El Hajji Diffusion equation for composite materials Electronic Journal of Differential Equations Diffusion equation composite material asymptotic behavior $H^0$-convergence.
author_facet	Mohamed El Hajji
author_sort	Mohamed El Hajji
title	Diffusion equation for composite materials
title_short	Diffusion equation for composite materials
title_full	Diffusion equation for composite materials
title_fullStr	Diffusion equation for composite materials
title_full_unstemmed	Diffusion equation for composite materials
title_sort	diffusion equation for composite materials
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2000-02-01
description	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 ${mathbb R}^N$, 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 $lim_{varepsilono 0}{r_varepsilon/varepsilon}=0$ with nonzero-average data.
topic	Diffusion equation composite material asymptotic behavior $H^0$-convergence.
url	http://ejde.math.txstate.edu/Volumes/2000/15/abstr.html
work_keys_str_mv	AT mohamedelhajji diffusionequationforcompositematerials
_version_	1725668259865296896

Diffusion equation for composite materials

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