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- Title
Asymptotic behavior of stationary solutions to elastic wave equations in a perturbed half‐space in ℝ<sup>3</sup>.
- Authors
Isozaki, Hiroshi; Kadowaki, Mitsuteru; Watanabe, Michiyuki
- Abstract
We study the stationary elastic wave equation with free boundary condition in a locally perturbed half‐space in ℝ3$$ {\mathrm{\mathbb{R}}}&#x0005E;3 $$. 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 핊+2. 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 B∗$$ {\mathcal{B}}&#x0005E;{\ast } $$ and derive their spatial asymptotics.
- Subjects
HELMHOLTZ, Hermann von, 1821-1894; ELASTIC waves; STANDING waves; RESOLVENTS (Mathematics); SCATTERING amplitude (Physics); HELMHOLTZ equation; RAYLEIGH waves; WAVE equation
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 15, p16318
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9452