Asymptotic behavior of stationary solutions to elastic wave equations in a perturbed half-space in R3

Hiroshi, Isozaki; Mitsuteru, Kadowaki; Michiyuki, Watanabe

We study the stationary elastic wave equation with free boundary condition in a locally perturbed half-space in ℝ^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 ?^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^∗ and derive their spatial asymptotics.

Mathematical Methods in the Applied Sciences

Wiley-Blackwell

1

63

https://doi.org/10.1002/mma.9452