ON NEW SURFACE-LOCALIZED TRANSMISSION EIGENMODES

作者：Deng, Youjun; Jiang, Yan; Liu, Hongyu^*; Zhang, Kai^*

来源：Inverse Problems and Imaging, 2022, 16(3): 595-611.

DOI：10.3934/ipi.2021063

• Transmission eigenfunctions
• spectral geometry
• surface localization
• wave concentration

Consider the transmission eigenvalue problem (Delta + k(2)n(2)) w = 0, (Delta + k(2)) v = 0 in Omega; w = v, partial derivative(nu)w = partial derivative(nu)v on partial derivative Omega. It is shown in [16] that there exists a sequence of eigenfunctions (w(m), v(m)) m is an element of N associated with k(m)->infinity such that either {w(m)} m is an element of N or {vm} m is an element of N are surfacelocalized, depending on n > 1 or 0 < n < 1. In this paper, we discover a new type of surface-localized transmission eigenmodes by constructing a sequence of transmission eigenfunctions (w(m), v(m)) m is an element of N associated with k(m) -> infinity such that both {w(m)} m is an element of N and {vm} m is an element of N are surface-localized, no matter n > 1 or 0 < n < 1. Though our study is confined within the radial geometry, the construction is subtle and technical.

• 单位
  吉林大学