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Worst scenario method in homogenization. Linear case. (English) Zbl 1164.35317
Summary: 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 the stochastic approach to the problem, we use the worst scenario method due to I. 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 the generalized gradient in the places where these components change and on the average of the homogenized solution in some critical subdomain.

MSC:
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35B40 Asymptotic behavior of solutions to PDEs
35J25 Boundary value problems for second-order elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
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