Abstract
We first introduce the Lamé system that governs the elastic wave propagation in \(\mathbb {R}^n\), \(n=2, 3\). Throughout, we let \(\mathscr {C}\) and \(\rho \) signify the constitutive material parameters of an elastic medium. Here, \(\mathscr {C}(\textbf{x})=(\mathscr {C}_{ijkl}(\textbf{x}))_{i,j,k,l=1}^n\) is a four-rank real-valued tensor satisfying the following symmetry property.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C.J. Alves, R. Kress, On the far-field operator in elastic obstacle scattering. IMA J. Appl. Math. 67, 1–21 (2002)
J.H. Bramble, J.E. Pasciak, A note on the existense and uniqueness of solutions of frequency domain elastic problems: A prior estimate in \(H^{1}\). J. Math. Anal. Appl. 345, 396–404 (2008)
A. Charalambopoulos, On the interior transmission problem in nondissipative, inhomogeneous, anisotropic elasticity. J. Elast. Phys. Sci. Solids 67, 149–170 (2002)
Z. Chen, X. **ang, X. Zhang, Convergence of the PML method for elastic wave scattering problems. Math. Comput. 85, 2687–2714 (2016)
D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd edn. (Springer, New York, 1998)
P. Häner, On the uniqueness of the shape of a penetrable, anisotropic obstacle. J. Comput. Appl. Math. 116, 167–181 (2000)
P. Häner, On acoustic, electromagnetic, and elastic scattering problems in inhomogeneous media. Universität Göttingen, Habilitation Thesis (1998)
V.D. Kupradze et al., Three-dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity (North-Holland, Amsterdam, 1979)
W. McLean, Strongly Elliptic Systems and Boundary Integral Equations (Cambridge University Press, Cambridge, 2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2023 Science Press
About this chapter
Cite this chapter
Li, J., Liu, H. (2023). Direct Elastic Scattering Problems. In: Numerical Methods for Inverse Scattering Problems. Springer, Singapore. https://doi.org/10.1007/978-981-99-3772-1_6
Download citation
DOI: https://doi.org/10.1007/978-981-99-3772-1_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-3771-4
Online ISBN: 978-981-99-3772-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)