Stochastic homogenization of a class of monotone eigenvalue problems

Svanstedt, Nils

doi:10.1007/s10492-010-0014-8

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2012

2024

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“…The methods can be divided into two groups: in the first group the structure is supposed to be non-periodic but deterministic, the second one assumes a stochastic character of the structure, see, e.g. [12].…”

Section: Introductionmentioning

confidence: 99%

Outline of Nguetseng's approach to non-periodic homogenization

Franců¹

2012

Math. Appl.

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Abstract. Classical homogenization theory developed for modeling heterogeneous media with regular fine structure is based on the assumption that the structure is periodic. Since the structure of real materials is not perfectly periodic, several approaches were proposed. The approach proposed by Gabriel Nguetseng in 2003 seems to be the most general deterministic approach, it covers periodic, almostperiodic and other structures. It is based on the notion of Banach algebra spectrum. The aim of this survey paper is to give a brief self-contained outline of this rather complicated approach described in many-page papers.

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Section: Introductionmentioning

confidence: 99%