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A mathematical study of a hyperbolic metamaterial in free space

Patrick Ciarlet 1 Maryna Kachanovska 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : Wave propagation in hyperbolic metamaterials is described by the Maxwell equations with a frequency dependent tensor of dielectric permittivity, whose eigenvalues are of different signs. In this case the problem becomes hyperbolic (Klein-Gordon equation) for a certain range of frequencies. The principal theoretical and numerical difficulty comes from the fact that this hyperbolic equation is posed in a free space, without initial conditions provided. The subject of the work is the theoretical justification of this problem. In particular, this includes the construction of a radiation condition, a well-posedness result, a limiting absorption principle and regularity estimates on the solution.
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Contributor : Maryna Kachanovska <>
Submitted on : Wednesday, March 10, 2021 - 9:49:16 AM
Last modification on : Monday, March 29, 2021 - 2:55:18 PM
Long-term archiving on: : Friday, June 11, 2021 - 6:20:56 PM


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  • HAL Id : hal-03164619, version 1



Patrick Ciarlet, Maryna Kachanovska. A mathematical study of a hyperbolic metamaterial in free space. 2021. ⟨hal-03164619⟩



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