Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)629-659
Journal / PublicationJournal of Differential Equations
Volume371
Online published18 Jul 2023
Publication statusPublished - 25 Oct 2023

Abstract

We are concerned with a coupled-physics spectral problem arising in the coupled propagation of acoustic and elastic waves, which is referred to as the acoustic-elastic transmission eigenvalue problem. There are two major contributions in this work which are new to the literature. First, under a mild condition on the medium parameters, we prove the existence of an acoustic-elastic transmission eigenvalue. Second, we establish a geometric rigidity result of the transmission eigenfunctions by showing that they tend to localize on the boundary of the underlying domain. Moreover, we also consider interesting implications of the obtained results to the effective construction of metamaterials by using bubbly elastic structures and to the inverse problem associated with the fluid-structure interaction. © 2023 Elsevier Inc.

Research Area(s)

  • Acoustic-elastic, Boundary localization, Bubbly elastic medium, Spectral geometry, Transmission eigenfunctions, Transmission eigenvalues

Citation Format(s)

Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications. / Diao, Huaian; Li, Hongjie; Liu, Hongyu et al.
In: Journal of Differential Equations, Vol. 371, 25.10.2023, p. 629-659.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review