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Inverse spectral Love problem via Weyl-Titchmarsh function
Malmö University, Faculty of Technology and Society (TS), Department of Materials Science and Applied Mathematics (MTM). Lund Univ, Ctr Math Sci, S-22100 Lund, Sweden.ORCID iD: 0009-0002-4321-1580
2024 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 480, no 2299, article id 20240240Article in journal (Refereed) Published
Abstract [en]

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 Schr & ouml;dinger equation with Robin boundary conditions on the half-line. The goal of the paper is to establish a method to recover the potential from eigenvalues and resonances through 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.

Place, publisher, year, edition, pages
Royal Society, 2024. Vol. 480, no 2299, article id 20240240
Keywords [en]
inverse problems, resonances, Sturm-Liouville problems, Love surface waves, Weyl-Titchmarsh function, spectral problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mau:diva-71674DOI: 10.1098/rspa.2024.0240ISI: 001328100800003OAI: oai:DiVA.org:mau-71674DiVA, id: diva2:1907314
Available from: 2024-10-22 Created: 2024-10-22 Last updated: 2024-10-22Bibliographically approved

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Sottile, Samuele

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