English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate the eigenvalue problem $-\text{div}(\sigma \nabla u) = \lambdau\ (\mathscr{P})$ in a 2D domain $\Omega$ divided into two regions$\Omega_{\pm}$. We are interested in situations where $\sigma$ takes positivevalues on $\Omega_{+}$ and negative ones on $\Omega_{-}$. Such problems appearin time harmonic electromagnetics in the modeling of plasmonic technologies. Ina recent work [15], we highlighted an unusual instability phenomenon for thesource term problem associated with $(\mathscr{P})$: for certainconfigurations, when the interface between the subdomains $\Omega_{\pm}$presents a rounded corner, the solution may depend critically on the value ofthe rounding parameter. In the present article, we explain this propertystudying the eigenvalue problem $(\mathscr{P})$. We provide an asymptoticexpansion of the eigenvalues and prove error estimates. We establish anoscillatory behaviour of the eigenvalues as the rounding parameter of thecorner tends to zero. We end the paper illustrating this phenomenon withnumerical experiments.

Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner