Asymptotic behavior of stationary solutions to elastic wave equations in a perturbed half‐space in ℝ 3

We study the stationary elastic wave equation with free boundary condition in a locally perturbed half‐space in . Using the stationary phase method, we derive an asymptotic behavior at infinity of the resolvent of the elastic operator uniformly with respect to the direction in . Consequently, the bo...

Full description

Saved in:
Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 46; no. 15; pp. 16318 - 16380
Main Authors Isozaki, Hiroshi, Kadowaki, Mitsuteru, Watanabe, Michiyuki
Format Journal Article
LanguageEnglish
Published 01.10.2023
Online AccessGet full text

Cover

More Information
Summary:We study the stationary elastic wave equation with free boundary condition in a locally perturbed half‐space in . Using the stationary phase method, we derive an asymptotic behavior at infinity of the resolvent of the elastic operator uniformly with respect to the direction in . Consequently, the body waves and the Rayleigh surface waves appear simultaneously in the expansion. From the far‐field pattern of the expansion, we obtain the scattering amplitude. We also characterize the space of generalized eigenfunctions in terms of Agmon–Hörmander space and derive their spatial asymptotics.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9452