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Non-periodic explicit homogenization and reduction of dimension: the linear case
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-3125-3030
2003 (English)In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 68, no 3, 269-298 p.Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to give explicit limit expressions, for diffusion equations involving a small parameter epsilon, describing both nonperiodic homogenization and reduction of dimension. In other words, we give the limit behaviour, when epsilon tends to zero, of the diffusion equation in a thin domain, with thickness of order epsilon, when the coefficients of the equation also depend on epsilon and may present rapid, nonperiodic oscillations, provided they satisfy a suitable compensated compactness condition. We consider two kinds of reduction of dimension: the case of thin plates (3D --> 2D) and the case of thin cylinders (3D --> 1D). In particular, we give the limit diffusion equation for laminated plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications.

Place, publisher, year, edition, pages
2003. Vol. 68, no 3, 269-298 p.
Keyword [en]
homogenization, reduction of dimension, compensated compactness, monotone problems, cylinders, model, convergence
URN: urn:nbn:se:kth:diva-22514ISI: 000182955300003OAI: diva2:341212
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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