Nonlinear interaction of waves in elastodynamics and an inverse problem
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We consider nonlinear elastic wave equations generalizing Gol’dberg’s five constants model. We analyze the nonlinear interaction of two distorted plane waves and characterize the possible nonlinear responses. Using the boundary measurements of the nonlinear responses, we solve the inverse problem of determining elastic parameters from the displacement-to-traction map.
Maarten V. de Hoop acknowledges and sincerely thanks the Simons Foundation under the MATH\(+\)X program for financial support. He was also partially supported by the members of the Geo-Mathematical Imaging Group at Rice University and NSF under grant DMS-1815143. Gunther Uhlmann is partially supported by NSF and a Si-Yuan Professorship at HKUST.
- 4.Gol’dberg, Z.A.: Interaction of plane longitudinal and transverse elastic waves. Sov. Phys. Acoust. 6(3), 306–310 (1961)Google Scholar
- 12.Landau, L., Lifshitz, E.M.: Theory of Elasticity, vol. 7. Course of Theoretical Physics 3, p. 109. Pergamon Press, Oxford (1986)Google Scholar
- 14.Melrose, R.: Differential analysis on manifolds with corners. Unpublished lecture notesGoogle Scholar
- 17.Norris, A.N.: Finite-amplitude waves in solids. Nonlinear Acoust. 9, 263–277 (1998)Google Scholar
- 22.Wang, Y., Zhou, T.: Inverse problems for quadratic derivative nonlinear wave equations. Commun. Partial Differ. Equ. (to appear) Google Scholar