耦合物理传输特征值问题及其谱性质及其应用

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-06-11 DOI:10.1016/j.jde.2025.113508

Huaian Diao , Hongyu Liu , Qingle Meng , Li Wang

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引用次数: 0

摘要

本文研究了一个耦合声学原理和弹性原理的传输本征值问题。在研究流固相互作用和构建气泡弹性结构以制造超材料时，自然会出现这个问题。在典型的正则性条件下，我们发现了传输本征函数在域角附近的有趣的局部几何结构。作为应用，我们给出了声弹性系统反问题的新颖的唯一可辨识性和可见性结果，具有实际意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics