ON NEW SURFACE-LOCALIZED TRANSMISSION EIGENMODES
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 595-611 |
| Journal / Publication | Inverse Problems and Imaging |
| Volume | 16 |
| Issue number | 3 |
| Online published | Oct 2021 |
| Publication status | Published - Jun 2022 |
Link(s)
Abstract
Consider the transmission eigenvalue problem (Δ + k2n2)w = 0, (Δ + k2)v = 0 in Ω; w = v, ∂vw = ∂vv on ∂Ω.
It is shown in [16] that there exists a sequence of eigenfunctions (wm, vm)m∈ℕ associated with km → ∞ such that either {wm}m∈ℕ or {vm}m∈ℕ are surface-localized, 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 (wm, vm)m∈ℕ associated with km → ∞ such that both {wm}m∈ℕ and {vm}m∈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.
It is shown in [16] that there exists a sequence of eigenfunctions (wm, vm)m∈ℕ associated with km → ∞ such that either {wm}m∈ℕ or {vm}m∈ℕ are surface-localized, 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 (wm, vm)m∈ℕ associated with km → ∞ such that both {wm}m∈ℕ and {vm}m∈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.
Research Area(s)
- Transmission eigenfunctions, spectral geometry, surface localization, wave concentration, CORNERS, SCATTERING, BESSEL, EIGENFUNCTIONS, UNIQUENESS, BOUNDS, ZEROS
Citation Format(s)
ON NEW SURFACE-LOCALIZED TRANSMISSION EIGENMODES. / Deng, Youjun; Jiang, Yan; Liu, Hongyu et al.
In: Inverse Problems and Imaging, Vol. 16, No. 3, 06.2022, p. 595-611.
In: Inverse Problems and Imaging, Vol. 16, No. 3, 06.2022, p. 595-611.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
