A nonuniqueness theorem for an inverse boundary value problem in elasticity

SIAM Journal on Applied Mathematics

Volumn 56, Issue 2, 1996, Pages 602-610

  Nakamura, Gen ^a   Tanuma, Kazumi ^b,c  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

^b EHIME UNIVERSITY   (Japan)

^c OSAKA KYOIKU UNIVERSITY   (Japan)

Author keywords

Dirichlet to Neumann map; Elastic tensor; Inverse boundary value problems; Surface impedance tensor

Indexed keywords

ANISOTROPY; BOUNDARY VALUE PROBLEMS; ELASTICITY; MATHEMATICAL MODELS; TENSORS;

DIRICHLET TO NEUMANN MAP; ELASTIC TENSOR; NONUNIQUENESS THEOREM; ORTHOTROPICAL MATERIAL; SURFACE IMPEDANCE TENSOR; TWO DIMENSIONAL ANISOTROPIC ELASTIC MEDIUM;

INVERSE PROBLEMS;

EID: 0030126876     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003613999426630X     Document Type: Article

References (10)

1. D. M. BARNETT AND J. LOTHE, Free surface (Rayleigh) waves in anisotropic elastic half-spaces: The surface impedance method, Proc. Royal Soc. London A, 402 (1985), pp. 135-152.
2. P. CHADWICK AND G. D. SMITH, Foundations of the theory of surface waves in anisotropic elastic materials, in Advances in Applied Mechanics, Vol. 17, C. H. Yih, ed., Academic Press, New York, 1977, pp. 303-376.
3. _, Surface waves in cubic elastic materials, in Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, H. G. Hopkins and M. J. Sewell, eds., Pergamon Press, Oxford, 1982, pp. 47-100.
4. G. DUVAUT AND J. L. LIONS, Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976.
5. A. E. GREEN AND W. ZERNA, Theoretical Elasticity, Oxford Univ. Press, London, 1954.
6. V. ISAKOV, Uniqueness and stability in multi-dimensional inverse problems, Inverse Problems, 9 (1993), pp. 579-621.
7. S. MIZOHATA, The Theory of Partial Differential Equations, Cambridge Univ. Press, Cambridge, 1973.
8. G. NAKAMURA, Existence and propagation of Rayleigh waves and pulses, in Modern Theory of Anisotropic Elasticity and Applications, J. J. Wu, T. C. T. Ting, and D. M. Barnett, eds., Society for Industrial and Applied Mathematics, Philadelphia, 1991, pp. 215-231.
9. G. NAKAMURA AND G. UHLMANN, Inverse problems at the boundary for an elastic medium, SIAM J. Math. Anal., 26 (1995), pp. 263-279.
10. J. SYLVESTER AND G. UHLMANN, The Dirichlet to Neumann map and applications, in Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing, and W. Rundell, eds., Society for Industrial and Applied Mathematics, Philadelphia, 1990, pp. 101-139.