The analysis of resonant frequencies and blow-up estimates of close-to-touching subwavelength resonators in the two-dimensional Helmholtz system
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915628600786944 |
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| author | Dong, Hongjie Li, Hongjie Xu, Longjuan |
| author_facet | Dong, Hongjie Li, Hongjie Xu, Longjuan |
| contents | In this paper, we investigate wave scattering by a pair of closely spaced inclusions embedded in a homogeneous medium, characterized by a high contrast physical parameters. The system is modeled by the two-dimensional Helmholtz equation. We show that this configuration exhibits two sub-wavelength resonant modes, whose frequencies display distinct leading-order asymptotic behaviors. These findings differ significantly from those in the three-dimensional Helmholtz setting. Furthermore, we provide a quantitative analysis of the gradient blow-up rates for the wave field localized between the two resonators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The analysis of resonant frequencies and blow-up estimates of close-to-touching subwavelength resonators in the two-dimensional Helmholtz system Dong, Hongjie Li, Hongjie Xu, Longjuan Analysis of PDEs Mathematical Physics In this paper, we investigate wave scattering by a pair of closely spaced inclusions embedded in a homogeneous medium, characterized by a high contrast physical parameters. The system is modeled by the two-dimensional Helmholtz equation. We show that this configuration exhibits two sub-wavelength resonant modes, whose frequencies display distinct leading-order asymptotic behaviors. These findings differ significantly from those in the three-dimensional Helmholtz setting. Furthermore, we provide a quantitative analysis of the gradient blow-up rates for the wave field localized between the two resonators. |
| title | The analysis of resonant frequencies and blow-up estimates of close-to-touching subwavelength resonators in the two-dimensional Helmholtz system |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2511.16387 |