Inverse spectral Love problem via Weyl-Titchmarsh function
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910644309065728 |
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| author | Sottile, Samuele |
| author_facet | Sottile, Samuele |
| contents | In this paper we prove an inverse resonance theorem for the half-solid with vanishing stresses on the surface via Weyl-Titchmarsh function. Using a semi-classical approach it is possible to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. The goal of the paper is to establish a method to recover the potential from the Weyl-Titchmarsh function for non self-adjoint problems and to establish a one-to-one and onto map between suitable function spaces. Moreover, we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances, via the spectral data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14653 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inverse spectral Love problem via Weyl-Titchmarsh function Sottile, Samuele Spectral Theory Mathematical Physics Analysis of PDEs 35R30, 35Q86, 34A55, 34L25, 81U40, 74J25 In this paper we prove an inverse resonance theorem for the half-solid with vanishing stresses on the surface via Weyl-Titchmarsh function. Using a semi-classical approach it is possible to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. The goal of the paper is to establish a method to recover the potential from the Weyl-Titchmarsh function for non self-adjoint problems and to establish a one-to-one and onto map between suitable function spaces. Moreover, we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances, via the spectral data. |
| title | Inverse spectral Love problem via Weyl-Titchmarsh function |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs 35R30, 35Q86, 34A55, 34L25, 81U40, 74J25 |
| url | https://arxiv.org/abs/2312.14653 |