On a coupled-physics transmission eigenvalue problem and its spectral properties with applications

Huaian Diao; Hongyu Liu; Qingle Meng; Li Wang

doi:10.1016/j.jde.2025.113508

On a coupled-physics transmission eigenvalue problem and its spectral properties with applications

Huaian Diao
, Hongyu Liu
, Qingle Meng
, Li Wang^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to create metamaterials. We uncover intriguing local geometric structures of the transmission eigenfunctions near the corners of the domains, under typical regularity conditions. As applications, we present novel unique identifiability and visibility results for an inverse problem associated with an acoustoelastic system, which hold practical significance. © 2025 Elsevier Inc.

Original language	English
Article number	113508
Journal	Journal of Differential Equations
Volume	441
Online published	11 Jun 2025
DOIs	https://doi.org/10.1016/j.jde.2025.113508
Publication status	Published - 5 Oct 2025

Bibliographical note

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© 2025 Elsevier Inc.

Funding

We would like to express our sincere gratitude to the anonymous referee for his/her constructive comments and valuable suggestions, which have significantly improved the presentation of this paper. The work of H. Diao is supported by National Natural Science Foundation of China (No. 12371422) and the Fundamental Research Funds for the Central Universities, JLU. The work of H. Liu is supported by the NSFC/RGC Joint Research Scheme, N_CityU101/21; ANR/RGC Joint Research Scheme, A_CityU203/19; and the Hong Kong RGC General Research Funds (projects 11311122, 11300821 and 11304224). The work of Q. Meng is supported by the Hong Kong RGC Postdoctoral Fellowship Scheme (No.: PDFS2324-1S09).

Research Keywords

Acoustoelastic
Corner singularity
Inverse inclusion problem
Spectral geometry
Transmission eigenvalue problem
Unique identifiability

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RGC-funded

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abstract = "In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to create metamaterials. We uncover intriguing local geometric structures of the transmission eigenfunctions near the corners of the domains, under typical regularity conditions. As applications, we present novel unique identifiability and visibility results for an inverse problem associated with an acoustoelastic system, which hold practical significance. {\textcopyright} 2025 Elsevier Inc.",

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AU - Diao, Huaian

AU - Liu, Hongyu

AU - Meng, Qingle

AU - Wang, Li

PY - 2025/10/5

Y1 - 2025/10/5

N2 - In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to create metamaterials. We uncover intriguing local geometric structures of the transmission eigenfunctions near the corners of the domains, under typical regularity conditions. As applications, we present novel unique identifiability and visibility results for an inverse problem associated with an acoustoelastic system, which hold practical significance. © 2025 Elsevier Inc.

AB - In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to create metamaterials. We uncover intriguing local geometric structures of the transmission eigenfunctions near the corners of the domains, under typical regularity conditions. As applications, we present novel unique identifiability and visibility results for an inverse problem associated with an acoustoelastic system, which hold practical significance. © 2025 Elsevier Inc.

KW - Acoustoelastic

KW - Corner singularity

KW - Inverse inclusion problem

KW - Spectral geometry

KW - Transmission eigenvalue problem

KW - Unique identifiability

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U2 - 10.1016/j.jde.2025.113508

DO - 10.1016/j.jde.2025.113508

M3 - RGC 21 - Publication in refereed journal

AN - SCOPUS:105007637891

SN - 0022-0396

VL - 441

JO - Journal of Differential Equations

JF - Journal of Differential Equations

M1 - 113508

ER -

On a coupled-physics transmission eigenvalue problem and its spectral properties with applications

Abstract

Bibliographical note

Funding

Research Keywords

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GRF: A Mathematical Theory of Inverse Problems for Mean Field Games

GRF: Mathematical Study of Fields Concentration and Gradient Estimates with Applications

GRF: Mathematical Studies of Surface-localized Transmission Eigenstates and Applications

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On a coupled-physics transmission eigenvalue problem and its spectral properties with applications

Abstract

Bibliographical note

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

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Projects

GRF: A Mathematical Theory of Inverse Problems for Mean Field Games

GRF: Mathematical Study of Fields Concentration and Gradient Estimates with Applications

GRF: Mathematical Studies of Surface-localized Transmission Eigenstates and Applications

Cite this