Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 60, pp. 1-18.

Title: Asymptotic analysis of  sign-changing transmission problems with rapidly oscillating interface

Authors: Renata Bunoiu (Univ. de Lorraine, Metz, France)
         Karim Ramdani (Univ. de Lorraine, Metz, France)
         Claudia Timofte (Univ. of Bucharest, Romania)

Abstract: 
We study the asymptotic behavior of a  sign-changing transmission problem, 
stated in a symmetric oscillating domain obtained by gluing together a 
positive and a negative material, separated by an imperfect and rapidly 
oscillating interface. 
The interface separating  the two heterogeneous materials has a periodic 
microstructure and  is a small perturbation of a flat interface. 
The solution of the transmission problem is continuous and its flux has a 
jump on the oscillating interface. Under certain conditions on the 
properties of the two materials, we derive the limit problem and we prove 
the convergence result. The T-coercivity method is used to 
handle the lack of coercivity for both the microscopic and the macroscopic 
limit problems.


Submitted September 24, 2024. Published October 11, 2024.
Math Subject Classifications: 35B40, 35Q60, 78M35
Key Words: Positive and negative materials; transmission problem; asymptotic analysis; oscillating interface; imperfect interfaces; flux jump