On Ventcel-type transmission conditions for a Helmholtz problem with a non-uniform thin layer

• Khaled El-Ghaouti Boutarene ^[2] ; Sami Galleze ^[2] ; Victor Péron ^[1]
  1. [1] University of Pau and Pays de l'Adour

     University of Pau and Pays de l'Adour

     Arrondissement de Pau, Francia

     
  2. [2] AMNEDP Laboratory, Faculty of Mathematics, USTHB
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 82, Nº. 3, 2025, págs. 421-454
• Idioma: inglés
• DOI: 10.1007/s40324-024-00358-4
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• Resumen

  • We study the asymptotic behaviour of the electric field in the transverse magnetic (TM) mode, propagating in a material composed of a two-dimensional object surrounded by a thin layer of non-constant thickness and embedded in an ambient medium. Using an asymptotic expansion of the solution uε to the Helmholtz problem, we derive Ventcel-type transmission conditions on the limit interface Γ modelling the effect of the thin layer with accuracy up to O(ε2).