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Worst scenario method in homogenization. Linear case

Luděk Nechvátal (2006)

Applications of Mathematics

The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite materials with periodic structure. Instead of stochastic approach to the problem, we use the worst scenario method due to Hlaváček (method of reliable solution). A few criterion functionals are introduced. We focus on the range of the homogenized coefficients from knowledge of the ranges of individual components in the composite, on the values of generalized...

Σ -convergence of nonlinear monotone operators in perforated domains with holes of small size

Jean Louis Woukeng (2009)

Applications of Mathematics

This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in N with isolated holes of size ε 2 ( ε > 0 a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual periodic perforation of the domain and the classical periodicity hypothesis on the coefficients of the operator...

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