Direct resonance problem for Rayleigh seismic surface waves
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910541416497152 |
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| author | Sottile, Samuele |
| author_facet | Sottile, Samuele |
| contents | In this paper we study the direct resonance problem for Rayleigh seismic surface waves and obtain a constraint on the location of resonances and establish a forbidden domain as the main result. In order to obtain the main result we make a Pekeris-Markushevich transformation of the Rayleigh system with free surface boundary condition such that we get a matrix Schrödinger-type form of it. We obtain parity and analytical properties of its fundamental solutions, which are needed to prove the main theorem. We construct a function made up by Rayleigh determinants factors, which is proven to be entire, of exponential type and in the Cartwright class and leads to the constraint on the location of resonances. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_17580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct resonance problem for Rayleigh seismic surface waves Sottile, Samuele Analysis of PDEs Mathematical Physics Spectral Theory 35R30, 35Q86, 34A55, 34L25, 74J25 In this paper we study the direct resonance problem for Rayleigh seismic surface waves and obtain a constraint on the location of resonances and establish a forbidden domain as the main result. In order to obtain the main result we make a Pekeris-Markushevich transformation of the Rayleigh system with free surface boundary condition such that we get a matrix Schrödinger-type form of it. We obtain parity and analytical properties of its fundamental solutions, which are needed to prove the main theorem. We construct a function made up by Rayleigh determinants factors, which is proven to be entire, of exponential type and in the Cartwright class and leads to the constraint on the location of resonances. |
| title | Direct resonance problem for Rayleigh seismic surface waves |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory 35R30, 35Q86, 34A55, 34L25, 74J25 |
| url | https://arxiv.org/abs/2407.17580 |