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Title: Homogenization of the Maxwell Equations: Case II. Nonlinear conductivity (English)
Author: Wellander, Niklas
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 47
Issue: 3
Year: 2002
Pages: 255-283
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: nonlinear PDEs
Keyword: Maxwell’s equations
Keyword: nonlinear conductivity
Keyword: homogenization
Keyword: existence of solution
Keyword: unique solution
Keyword: two-scale convergence
Keyword: corrector results
Keyword: heterogeneous materials
Keyword: compactness result
Keyword: non-periodic medium
MSC: 35B27
MSC: 35Q60
MSC: 74Q10
MSC: 74Q15
MSC: 78A25
idZBL: Zbl 1090.35504
idMR: MR1900514
DOI: 10.1023/A:1021797505024
Date available: 2009-09-22T18:10:11Z
Last updated: 2015-05-19
Stable URL:
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