Niklas Wellander (2001)
Applications of Mathematics
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The Maxwell equations in a heterogeneous medium are studied. Nguetseng’s method of two-scale convergence is applied to homogenize and prove corrector results for the Maxwell equations with inhomogeneous initial conditions. Compactness results, of two-scale type, needed for the homogenization of the Maxwell equations are proved.
H. Attouch, G. Buttazzo (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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...
G. A. Yosifian (2001)
Rendiconti del Seminario Matematico della Università di Padova
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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...