Electron. J. Differential Equations, Vol. 2024 (2024), No. 60, pp. 1-18.
Asymptotic analysis of sign-changing transmission problems with rapidly oscillating interface
Renata Bunoiu, Karim Ramdani, Claudia Timofte
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.
DOI: 10.58997/ejde.2024.60
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Renata Bunoiu
Université de Lorraine
CNRS, IECL, F-57000 Metz, France
email: renata.bunoiu@univ-lorraine.fr
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Karim Ramdani
Université de Lorraine
CNRS, INRIA, IECL, F-54000 Nancy, France
email: karim.ramdani@inria.fr
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Claudia Timofte
University of Bucharest
Faculty of Physics
Bucharest-Magurele, P.O. Box MG-11, Romania
email: claudia.timofte@g.unibuc.ro
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