Homogenisation for a statinory Maxwell system

2011/01/27 by A. A. Pozharskiĭ, Alexey A. Pozharskii, Pozharskii, Alexey A.
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1101.5267

arxiv created 2011/01/27 · openalex publication_date 2011/01/27 · arxiv updated 2011/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study homogenization problem for the stationary Maxwell system. It is supposed that the magnetic permeability and the dielectric permittivity locally close to fast-oscillating (with respect to some small parameter) periodic functions which can change the form on rather big distances. An asymptotic behavior to solutions of the Maxwell system outside of its spectrum is obtained. We also describe asymptotic behavior of resolvent with control of the remainder in terms of some appropriate operator norms.

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