Interior Transmission Resonance

Youjun Deng and Hongyu Liu
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Youjun Deng: Central South University, School of Mathematics and Statistics
Hongyu Liu: City University of Hong Kong, Department of Mathematics

Chapter Chapter 6 in Spectral Theory of Localized Resonances and Applications, 2024, pp 281-356 from Springer

Abstract: Abstract In this chapter, we consider the interior transmission eigenvalue problem. Our focus is on justifying that the transmission eigenfunctions form a certain interior resonant modes. In fact, the results in this chapter show that the transmission eigenfunctions generically oscillate at frequencies much higher than the operating frequency, which is a typical resonance behaviour. Moreover, the high oscillation tend to localize on the boundary of the underlying the domain.

Date: 2024
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DOI: 10.1007/978-981-99-6244-0_6

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