Recovery of discontinuous Lamé parameters from exterior Cauchy data

References

• Belishev, M. I. (1987). An approach to multidimensional inverse problems for the wave equation. Dokl. Akad. Nauk SSSR. 297(3):524–527.
   Google Scholar
• Stefanov, P., Uhlmann, G. (1998). Rigidity for metrics with the same lengths of geodesics. Math. Res. Lett. 5(1):83–96. DOI: 10.4310/MRL.1998.v5.n1.a7.
   Web of Science ®Google Scholar
• Uhlmann, G., Vasy, A. (2016). The inverse problem for the local geodesic ray transform. Invent. math. 205(1):83–120. DOI: 10.1007/s00222-015-0631-7.
   Web of Science ®Google Scholar
• Caday, P., de Hoop, M. V., Katsnelson, V., Uhlmann, G. (2019). Scattering control for the wave equation with unknown wave speed. Arch. Rational Mech. Anal. 231(1):409–464. DOI: 10.1007/s00205-018-1283-8.
   Web of Science ®Google Scholar
• Caday, P., de Hoop, M. V., Katsnelson, V., Uhlmann, G. (2019). Reconstruction of piecewise smooth wave speeds using multiple scattering. Trans. Amer. Math. Soc. 372(2):1213–1235. DOI: 10.1090/tran/7632.
   Web of Science ®Google Scholar
• Rachele, L. V. (2000). An inverse problem in elastodynamics: uniqueness of the wave speeds in the interior. J. Differential Equations. 162(2):300–325. DOI: 10.1006/jdeq.1999.3657.
   Web of Science ®Google Scholar
• Hansen, S., Uhlmann, G. (2003). Propagation of polarization in elastodynamics with residual stress and travel times. Math. Ann. 326(3):563–587. DOI: 10.1007/s00208-003-0437-6.
   Web of Science ®Google Scholar
• Rachele, L. V. (2000). Boundary determination for an inverse problem in elastodynamics. Comm. Partial Differential Equations. 25:1951–1996.
   Web of Science ®Google Scholar
• Stefanov, P., Uhlmann, G., Vasy, A. (2015). Boundary rigidity with partial data. J. Amer. Math. Soc. 29(2):299–332. DOI: 10.1090/jams/846.
   Web of Science ®Google Scholar
• Agranovsky, M., Kuchment, P. (2007). Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed. Inverse Prob. . 23(5):2089–2102. DOI: 10.1088/0266-5611/23/5/016.
   Web of Science ®Google Scholar
• Kuchment, P., Kunyansky, L. (2015). Mathematics of photoacoustic and thermoacoustic tomography. In Handbook of Mathematical Methods in Imaging. Vols. 1–3. New York, NY: Springer, pp. 1117–1167.
   Google Scholar
• Stefanov, P., Uhlmann, G. (2009). Thermoacoustic tomography with variable sound speed. Inverse Prob. . 25(7):075011–075016. DOI: 10.1088/0266-5611/25/7/075011.
   Web of Science ®Google Scholar
• Stefanov, P., Uhlmann, G. (2011). Thermoacoustic tomography arising in brain imaging. Inverse Prob. . 27(4):045004–045026. DOI: 10.1088/0266-5611/27/4/045004.
   Web of Science ®Google Scholar
• Tittelfitz, J. (2012). Thermoacoustic tomography in elastic media. Inverse Prob. 28(5):055004–055013. DOI: 10.1088/0266-5611/28/5/055004.
   Web of Science ®Google Scholar
• Wapenaar, K. (2014). Single-sided marchenko focusing of compressional and shear waves. Phys Rev E Stat Nonlin Soft Matter Phys. 90(6):063202–063Dec. DOI: 10.1103/PhysRevE.90.063202.
   PubMed Web of Science ®Google Scholar
• Belishev, M. I. (2006). Dynamical inverse problem for a Lamé type system. J. Inverse Ill-Posed Probl. 14(8):751–766. DOI: 10.1515/156939406779768300.
   Google Scholar
• Belishev, M. I. (1997). Boundary control in reconstruction of manifolds and metrics (the BC method). Inverse Prob. . 13(5):R1–R45. DOI: 10.1088/0266-5611/13/5/002.
   Web of Science ®Google Scholar
• Belishev, M. I., Gotlib, V. Y. (1999). Dynamical variant of the BC-method: theory and numerical testing. J. Inverse Ill-Posed Probl. 7(3):221–240.
   Google Scholar
• Stefanov, P., Uhlmann, G., Vasy, A. The transmission problem in linear isotropic elasticity. Preprint, (2019). https://arxiv.org/abs/1702.03842.
   Google Scholar
• Stefanov, P., Uhlmann, G., Vasy, A. (2018). Local recovery of the compressional and shear speeds from the hyperbolic DN map. Inverse Prob. . 34(1):014003–014013. DOI: 10.1088/1361-6420/aa9833.
   Web of Science ®Google Scholar
• Rachele, L. V. (2003). Uniqueness of the density in an inverse problem for isotropic elastodynamics. Trans. Amer. Math. Soc. 355(12):4781–4806. DOI: 10.1090/S0002-9947-03-03268-9.
   Web of Science ®Google Scholar
• Stefanov, P., Uhlmann, G., Vasy, A. (2018). Inverting the local geodesic x-ray transform on tensors. JAMA. 136(1):151–208. DOI: 10.1007/s11854-018-0058-3.
   Web of Science ®Google Scholar
• de Hoop, M. V., Ilmavirta, J. (2017). Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds. Inverse Prob. . 33(12):124003–124036. DOI: 10.1088/1361-6420/aa9423.
   Web of Science ®Google Scholar
• Ranjan, A., Shah, H. (2002). Convexity of spheres in a manifold without conjugate points. Proc. Math. Sci. 112(4):595–599. DOI: 10.1007/BF02829692.
   Google Scholar
• Hansen, S. (1991). Solution of a hyperbolic inverse problem by linearization. Comm. Partial Differential Equations. 16(2-3):291–309. DOI: 10.1080/03605309108820760.
   Web of Science ®Google Scholar
• Dencker, N. (1982). On the propagation of polarization sets for systems of real principal type. J. Funct. Anal. 46(3):351–372. DOI: 10.1016/0022-1236(82)90051-9.
   Web of Science ®Google Scholar
• Stolk, C. C. (2001). On the modeling and inversion of seismic data [PhD thesis]. University of Utrecht.
   Google Scholar
• Taylor, M. E. (1975). Reflection of singularities of solutions to systems of differential equations. Comm. Pure Appl. Math. 28(4):457–478. DOI: 10.1002/cpa.3160280403.
   Web of Science ®Google Scholar
• Yamamoto, K. (1989). Elastic waves in two solids as propagation of singularities phenomenon. Nagoya Math. J. 116:25–42. DOI: 10.1017/S0027763000001677.
   Web of Science ®Google Scholar