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An expansion theorem for two‐dimensional elastic waves and its application
Author(s) -
Chen KunChu,
Lin ChingLung
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.753
Subject(s) - mathematics , helmholtz equation , obstacle , mathematical analysis , amplitude , section (typography) , helmholtz free energy , calculus (dental) , physics , law , boundary value problem , computer science , optics , quantum mechanics , political science , operating system , medicine , dentistry
We prove an Atkinson–Wilcox‐type expansion for two‐dimensional elastic waves in this paper. The approach developed on the two‐dimensional Helmholtz equation will be applied in the proof. When the elastic fields are involved, the situation becomes much harder due to two wave solutions propagating at different phase velocities. In the last section, we give an application about the reconstruction of an obstacle from the scattering amplitude. Copyright © 2006 John Wiley & Sons, Ltd.