Homogenization of the Maxwell equations.

Autor:	Wellander, Niklas
Jazyk:	angličtina
Předmět:	matematika mathematics články journal articles 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
Druh dokumentu:	Non-fiction
ISSN:	0862-7940
Abstrakt:	Abstract: 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.
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Full text from SpringerLink