TY - JOUR
T1 - ON NEW SURFACE-LOCALIZED TRANSMISSION EIGENMODES
AU - Deng, Youjun
AU - Jiang, Yan
AU - Liu, Hongyu
AU - Zhang, Kai
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
KW - Transmission eigenfunctions
KW - spectral geometry
KW - surface localization
KW - wave concentration
KW - CORNERS
KW - SCATTERING
KW - BESSEL
KW - EIGENFUNCTIONS
KW - UNIQUENESS
KW - BOUNDS
KW - ZEROS
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85128259152&origin=recordpage
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U2 - 10.3934/ipi.2021063
DO - 10.3934/ipi.2021063
M3 - RGC 21 - Publication in refereed journal
VL - 16
SP - 595
EP - 611
JO - Inverse Problems and Imaging
JF - Inverse Problems and Imaging
SN - 1930-8337
IS - 3
ER -