Details
| Original language | English |
|---|---|
| Pages (from-to) | 2583-2633 |
| Number of pages | 51 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 377 |
| Issue number | 4 |
| Publication status | Published - Apr 2024 |
| Externally published | Yes |
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.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Transactions of the American Mathematical Society, Vol. 377, No. 4, 04.2024, p. 2583-2633.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The solid-fluid transmission problem
AU - Eptaminitakis, Nikolas
AU - Stefanov, Plamen
N1 - 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.
PY - 2024/4
Y1 - 2024/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85189110019&partnerID=8YFLogxK
U2 - 10.1090/tran/9016
DO - 10.1090/tran/9016
M3 - Article
AN - SCOPUS:85189110019
VL - 377
SP - 2583
EP - 2633
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 4
ER -