Communications in Mathematical Sciences

Volume 21 (2023)

Number 7

Homogenization of a transmission problem with sign-changing coefficients and interfacial flux jump

Pages: 2029 – 2049

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n7.a13

Authors

Renata Bunoiu (Université de Lorraine, CNRS, Institut Élie Cartan de Lorraine (IECL), Metz, France)

Karim Ramdani (Université de Lorraine, CNRS, Inria, IECL, Nancy, France)

Claudia Timofte (Faculty of Physics, University of Bucharest, Romania)

Abstract

We study the homogenization of a scalar problem posed in a composite medium made up of two materials, a positive and a negative one. An important feature is the presence of a flux jump across their oscillating interface. The main difficulties of this study are due to the sign-changing coefficients and the appearance of an unsigned surface integral term in the variational formulation. A proof by contradiction (nonstandard in this context) and T‑coercivity technics are used in order to cope with these difficulties.

Keywords

negative materials, transmission problem, homogenization, imperfect interfaces, flux jump

2010 Mathematics Subject Classification

35B27, 35Q60, 78M35, 80M35, 80M40

Received 2 July 2022

Received revised 6 January 2023

Accepted 6 February 2023

Published 9 October 2023