Limiting absorption principle and well-posedness for the time-harmonic Maxwell equations with anisotropic sign-changing coefficients. (English) Zbl 1451.35207
The authors study the limiting absorption principle and the well-posedness of Maxwell equations \(\nabla \times E = i\omega \mu H\) and \(\nabla \times H =- i\omega \varepsilon E+J\) in the space divided into a smooth domain \(D\) and \(D^-\), the complement of its closure to \(\mathbb R^3\). The permittivity \(\varepsilon\) and the permeability \(\mu\) are \((3\times 3)\) real, symmetric, uniformly elliptic matrix-valued functions in \(D\). The matrices have the form \(\varepsilon = \varepsilon^-+i \delta I\) and \(\mu=\mu^- +i \delta I\) in \(D^-\) where \(-\varepsilon^-\) and \(-\mu^-\) have the same properties as \(\varepsilon\), \(I\) is the identity matrix, \(\delta>0\). The authors obtain general conditions for \(\varepsilon\) and \(\mu\) for which the limiting absorption principle and the well-posedness hold. Applications to the stability of electromagnetic fields of negative-index metamaterials are discussed.
Reviewer: Vladimir Mityushev (Kraków)
MSC:
| 35Q61 | Maxwell equations |
| 78A25 | Electromagnetic theory (general) |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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