The solid-fluid transmission problem

verfasst von: Nikolas Eptaminitakis, Plamen Stefanov
Abstract: We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations describing the particle displacement and velocity in the solid, and pressure and velocity in the fluid, coupled by suitable transmission conditions at the interface. We show well-posedness for the coupled system and study the problem microlocally, constructing a parametrix for it using geometric optics. This construction describes the reflected and transmitted waves, including mode converted ones, related to incoming waves from either side. We also study formation of surface Scholte waves. Finally, we prove that under suitable assumptions, we can recover the s- and the p-speeds, as well as the speed of the liquid, from boundary measurements.
Externe Organisation(en): Purdue University
Typ: Artikel
Journal: Transactions of the American Mathematical Society
Band: 377
Seiten: 2583-2633
Anzahl der Seiten: 51
ISSN: 0002-9947
Publikationsdatum: 04.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Mathematik (insg.), Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2111.03218 (Zugang: Offen)
https://doi.org/10.1090/tran/9016 (Zugang: Geschlossen)

BibTeX

@article{130169292f444683808d4741e8dd3a7f,
title = "The solid-fluid transmission problem",
abstract = "We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations describing the particle displacement and velocity in the solid, and pressure and velocity in the fluid, coupled by suitable transmission conditions at the interface. We show well-posedness for the coupled system and study the problem microlocally, constructing a parametrix for it using geometric optics. This construction describes the reflected and transmitted waves, including mode converted ones, related to incoming waves from either side. We also study formation of surface Scholte waves. Finally, we prove that under suitable assumptions, we can recover the s- and the p-speeds, as well as the speed of the liquid, from boundary measurements.",
author = "Nikolas Eptaminitakis and Plamen Stefanov",
note = "Funding Information: Received by the editors December 4, 2021, and, in revised form, June 8, 2023. 2020 Mathematics Subject Classification. Primary 35A27, 35A18, 35A17, 35R30; Secondary 35Q86, 86A22. The second author was partly supported by NSF Grant DMS-1900475. ",
year = "2024",
month = apr,
doi = "10.1090/tran/9016",
language = "English",
volume = "377",
pages = "2583--2633",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "4",
}