Displaying similar documents to “Homogenization of the Maxwell equations: Case I. Linear theory”

Homogenization of the Maxwell Equations: Case II. Nonlinear conductivity

Niklas Wellander (2002)

Applications of Mathematics

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The Maxwell equations with uniformly monotone nonlinear electric conductivity in a heterogeneous medium, which may be non-periodic, are homogenized by two-scale convergence. We introduce a new set of function spaces appropriate for the nonlinear Maxwell system. New compactness results, of two-scale type, are proved for these function spaces. We prove existence of a unique solution for the heterogeneous system as well as for the homogenized system. We also prove that the solutions of...

Homogenization of parabolic equations an alternative approach and some corrector-type results

Anders Holmbom (1997)

Applications of Mathematics

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We extend and complete some quite recent results by Nguetseng [Ngu1] and Allaire [All3] concerning two-scale convergence. In particular, a compactness result for a certain class of parameterdependent functions is proved and applied to perform an alternative homogenization procedure for linear parabolic equations with coefficients oscillating in both their space and time variables. For different speeds of oscillation in the time variable, this results in three cases. Further, we prove...

Worst scenario method in homogenization. Linear case

Luděk Nechvátal (2006)

Applications of Mathematics

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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...