Boundary localization of transmission eigenfunctions in spherically stratified media

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)285-303
Journal / PublicationAsymptotic Analysis
Volume132
Issue number1-2
Online published2 Mar 2023
Publication statusPublished - 2023

Abstract

Consider the transmission eigenvalue problem for u∈H1(Ω) and v∈H1(Ω): ∇·(σ∇u)+k2n2u=0in Ω,Δv+k2v=0in Ω,u=v,σ∂u∂ν=∂v∂νon ∂Ω, where Ω is a ball in RN, N=2,3. If σ and n are both radially symmetric, namely they are functions of the radial parameter r only, we show that there exists a sequence of transmission eigenfunctions {um,vm}m∈N associated with km→+∞ as m→+∞ such that the L2-energies of vm’s are concentrated around ∂Ω. If σ and n are both constant, we show the existence of transmission eigenfunctions {uj,vj}j∈N such that both uj and vj are localized around ∂Ω. Our results extend the recent studies in (SIAM J. Imaging Sci. 14 (2021), 946–975; Chow et al.). Through numerics, we also discuss the effects of the medium parameters, namely σ and n, on the geometric patterns of the transmission eigenfunctions.

Research Area(s)

  • Transmission eigenfunctions, spectral geometry, boundary localization, wave localization, SCATTERING, CORNERS, BESSEL, ZEROS

Citation Format(s)

Boundary localization of transmission eigenfunctions in spherically stratified media. / Jiang, Yan; Liu, Hongyu; Zhang, Jiachuan et al.
In: Asymptotic Analysis, Vol. 132, No. 1-2, 2023, p. 285-303.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review