Titre : T-coercivity for scalar interface problems between dielectrics and metamaterials
Année : 2012
Type : article (revue avec comité de lecture)
Auteurs : A.-S. Bonnet-BenDhia, L. Chesnel, P. Ciarlet
Résumé : Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipa- tion is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of Rd, with d = 2, 3. Our aim is to characterize occurences where the problem is well-posed within the Fred- holm (or coercive + compact) framework. For that, we build some criteria, based on the geometry of the interface between the dielectric and the metamaterial. The proofs combine simple geometrical arguments with the approach of T-coercivity, introduced by the first and third authors and co-worker. Furthermore, the use of localization techniques allows us to derive well-posedness under conditions that involve the knowledge of the coefficients only near the interface. When the coefficients are piecewise constant, we establish the optimality of the criteria.
Thèmes : Ondes harmoniques
Référence : Math. Mod. Num. Anal. - vol. 46 (pp 1363–-1387 ) images/icons/doctype_pdf.gif