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

TL;DR

This paper studies a coupled-physics transmission eigenvalue problem combining acoustics and elasticity, revealing geometric properties of eigenfunctions and applying findings to inverse problems in acoustoelastic systems.

Contribution

It introduces a new coupled-physics eigenvalue problem, analyzes its spectral properties, and applies results to inverse problems with practical implications.

Findings

Eigenfunctions exhibit specific local geometric structures near domain corners.

Unique identifiability results are established for an associated inverse problem.

Visibility results for the inverse problem are demonstrated.

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.