The solid-fluid transmission problem

authored by: 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.
External Organisation(s): Purdue University
Type: Article
Journal: Transactions of the American Mathematical Society
Volume: 377
Pages: 2583-2633
No. of pages: 51
ISSN: 0002-9947
Publication date: 04.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.48550/arXiv.2111.03218 (Access: Open)
https://doi.org/10.1090/tran/9016 (Access: Closed)

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",
}