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Interior Transmission Resonance

In: Spectral Theory of Localized Resonances and Applications

Author

Listed:
  • Youjun Deng

    (Central South University, School of Mathematics and Statistics)

  • Hongyu Liu

    (City University of Hong Kong, Department of Mathematics)

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.

Suggested Citation

  • Youjun Deng & Hongyu Liu, 2024. "Interior Transmission Resonance," Springer Books, in: Spectral Theory of Localized Resonances and Applications, chapter 0, pages 281-356, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-6244-0_6
    DOI: 10.1007/978-981-99-6244-0_6
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