Abstract.
We show that knowing the displacement-to-traction map associated to the equations of isotropic elastodynamics with residual stress we can determine the lens maps of compressional and shear waves. We derive several consequences of this for the inverse problem of determining the residual stress and the Lamé parameters from the displacement-to-traction map.
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Received: 6 December 2001 / Revised version: 29 October 2002 / Published online: 8 April 2003
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ID="⋆" The author thanks the Department of Mathematics at the University of Washington for its hospitality during his visit in fall 2000.
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ID="⋆⋆" Partly supported by NSF grant DMS-0070488 and a John Simon Guggenheim fellowship. The author also thanks MSRI for partial support and for providing a very stimulating environment during the inverse problems program in fall 2001.
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Hansen, S., Uhlmann, G. Propagation of polarization in elastodynamics with residual stress and travel times. Math. Ann. 326, 563–587 (2003). https://doi.org/10.1007/s00208-003-0437-6
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DOI: https://doi.org/10.1007/s00208-003-0437-6