Geodesic
Homogenization of the Maxwell Equations: Case II. Nonlinear conductivity
Applications of Mathematics, Tome 47 (2002) no. 3, pp. 255-283.

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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 the heterogeneous system converge weakly to the solution of the homogenized system. Furthermore, we prove corrector results, important for numerical implementations.
DOI : 10.1023/A:1021797505024
Classification : 35B27, 35Q60, 74Q10, 74Q15, 78A25
Mots-clés : nonlinear PDEs; Maxwell’s equations; nonlinear conductivity; homogenization; existence of solution; unique solution; two-scale convergence; corrector results; heterogeneous materials; compactness result; non-periodic medium 
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Wellander, Niklas. Homogenization of the Maxwell Equations: Case II. Nonlinear conductivity. Applications of Mathematics, Tome 47 (2002) no. 3, pp. 255-283. doi : 10.1023/A:1021797505024. https://geodesic-test.mathdoc.fr/articles/10.1023/A:1021797505024/

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