Limiting absorption principle for a hybrid resonance in a two-dimensional cold plasma
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912653847298048 |
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| author | Kachanovska, Maryna Peillon, Étienne |
| author_facet | Kachanovska, Maryna Peillon, Étienne |
| contents | We study a limiting absorption principle for the boundary-value problem describing a hybrid plasma resonance, with a regular coefficient in the principal part of the operator that vanishes on a curve inside the domain and changes its sign across this curve. We prove the limiting absorption principle by establishing a priori bounds on the solution in certain weighted Sobolev spaces. Next, we show that the solution can be decomposed into regular and singular parts. A peculiar property of this decomposition enables us to introduce a radiation-like condition in a bounded domain and to state a well-posed problem satisfied by the limiting absorption solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_15153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limiting absorption principle for a hybrid resonance in a two-dimensional cold plasma Kachanovska, Maryna Peillon, Étienne Analysis of PDEs Mathematical Physics 35B65, 35B34, 35D40, 35M12, 35Q61 We study a limiting absorption principle for the boundary-value problem describing a hybrid plasma resonance, with a regular coefficient in the principal part of the operator that vanishes on a curve inside the domain and changes its sign across this curve. We prove the limiting absorption principle by establishing a priori bounds on the solution in certain weighted Sobolev spaces. Next, we show that the solution can be decomposed into regular and singular parts. A peculiar property of this decomposition enables us to introduce a radiation-like condition in a bounded domain and to state a well-posed problem satisfied by the limiting absorption solution. |
| title | Limiting absorption principle for a hybrid resonance in a two-dimensional cold plasma |
| topic | Analysis of PDEs Mathematical Physics 35B65, 35B34, 35D40, 35M12, 35Q61 |
| url | https://arxiv.org/abs/2510.15153 |