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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
Similarity:
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...