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Uniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type
1. | Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin |
2. | Weierstrass Institute, Mohrenstr. 39, 10117 Berlin |
3. | Graduate School of Mathematical Sciences University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914 |
References:
[1] |
G. Bao, H. Zhang and J. Zou, Unique determination of periodic polyhedral structures by scattered electromagnetic fields II: The resonance case, Trans. Amer. Math. Soc., 366 (2014), 1333-1361.
doi: 10.1090/S0002-9947-2013-05761-3. |
[2] |
A. Charalambopoulos, D. Gintides and K. Kiriaki, On the uniqueness of the inverse elastic scattering problem for periodic structures, Inverse Problems, 17 (2001), 1923-1935.
doi: 10.1088/0266-5611/17/6/323. |
[3] |
M. Costabel, M. Dauge and Y. Lafranche, Fast semi-analytic computation of elastic edge singularities, Computer Methods in Applied Mechanics and Engineering, 190 (2001), 2111-2134.
doi: 10.1016/S0045-7825(00)00226-7. |
[4] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Berlin, 1998.
doi: 10.1007/978-3-662-03537-5. |
[5] |
J. Elschner and G. Hu, Variational approach to scattering of plane elastic waves by diffraction gratings, Math. Meth. Appl. Sci., 33 (2010), 1924-1941.
doi: 10.1002/mma.1305. |
[6] |
J. Elschner and G. Hu, Global uniqueness in determining polygonal periodic structures with a minimal number of incident plane waves, Inverse Problems, 26 (2010), 115002, 23pp.
doi: 10.1088/0266-5611/26/11/115002. |
[7] |
J. Elschner and G. Hu, Inverse scattering of elastic waves by periodic structures: Uniqueness under the third or fourth kind boundary conditions, Meth. Appl. Anal., 18 (2011), 215-243.
doi: 10.4310/MAA.2011.v18.n2.a6. |
[8] |
J. Elschner and G. Hu, An optimization method in inverse elastic scattering for one-dimensional grating profiles, Commun. Comput. Phys., 12 (2012), 1434-1460. |
[9] |
J. Elschner and G. Hu, Elastic scattering by unbounded rough surfaces: Solvability in weighted Sobolev spaces, Appl. Anal., 94 (2015), 251-278.
doi: 10.1080/00036811.2014.887695. |
[10] |
J. Elschner, G. Schmidt and M. Yamamoto, Global uniqueness in determining rectangular periodic structures by scattering data with a single wave number, J. Inverse Ill-Posed Probl., 11 (2003), 235-244.
doi: 10.1515/156939403769237024. |
[11] |
F. Hettlich and A. Kirsch, Schiffer's theorem in inverse scattering for periodic structures, Inverse Problems, 13 (1997), 351-361.
doi: 10.1088/0266-5611/13/2/010. |
[12] |
G. Hu, Inverse wave scattering by unbounded obstacles: Uniqueness for the two-dimensional Helmholtz equation, Appl. Anal., 91 (2012), 703-717.
doi: 10.1080/00036811.2011.587811. |
[13] |
G. Hu, Y. Lu and B. Zhang, The factorization method for inverse elastic scattering from periodic structures, Inverse Problems, 29 (2013), 115005, 25pp.
doi: 10.1088/0266-5611/29/11/115005. |
[14] |
P. Grisvard, Singularités en élasticité, Arch. Rational Mech. Anal., 107 (1989), 157-180.
doi: 10.1007/BF00286498. |
[15] |
A. Kirsch, Diffraction by periodic structures, In 'Proc. Lapland Conf. Inverse Problems' (ed. L. Päivärinta et al), Springer, Berlin, Lecture Notes in Phys., 422 (1993), 87-102.
doi: 10.1007/3-540-57195-7_11. |
[16] |
C. B. Morrey, Jr. and L. Nirenberg, On the analyticity of the solutions of linear elliptic systems of partial differential equations, Communications on Pure and Applied Mathematics, 10 (1957), 271-290.
doi: 10.1002/cpa.3160100204. |
[17] |
S. Nakagawa, K. T. Nihei, L. R. Myer and E. L. Majer, Three-dimensional elastic wave scattering by a layer containing vertical periodic fractures, J. Acoust. Soc. Am., 113 (2003), 3012-3023.
doi: 10.1121/1.1572139. |
[18] |
A. Rössle, Corner singularities and regularity of weak solution for the two-dimensional Lamé equations on domains with angular corners, Journal of Elasticity, 60 (2000), 57-75.
doi: 10.1023/A:1007639413619. |
show all references
References:
[1] |
G. Bao, H. Zhang and J. Zou, Unique determination of periodic polyhedral structures by scattered electromagnetic fields II: The resonance case, Trans. Amer. Math. Soc., 366 (2014), 1333-1361.
doi: 10.1090/S0002-9947-2013-05761-3. |
[2] |
A. Charalambopoulos, D. Gintides and K. Kiriaki, On the uniqueness of the inverse elastic scattering problem for periodic structures, Inverse Problems, 17 (2001), 1923-1935.
doi: 10.1088/0266-5611/17/6/323. |
[3] |
M. Costabel, M. Dauge and Y. Lafranche, Fast semi-analytic computation of elastic edge singularities, Computer Methods in Applied Mechanics and Engineering, 190 (2001), 2111-2134.
doi: 10.1016/S0045-7825(00)00226-7. |
[4] |
D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Berlin, 1998.
doi: 10.1007/978-3-662-03537-5. |
[5] |
J. Elschner and G. Hu, Variational approach to scattering of plane elastic waves by diffraction gratings, Math. Meth. Appl. Sci., 33 (2010), 1924-1941.
doi: 10.1002/mma.1305. |
[6] |
J. Elschner and G. Hu, Global uniqueness in determining polygonal periodic structures with a minimal number of incident plane waves, Inverse Problems, 26 (2010), 115002, 23pp.
doi: 10.1088/0266-5611/26/11/115002. |
[7] |
J. Elschner and G. Hu, Inverse scattering of elastic waves by periodic structures: Uniqueness under the third or fourth kind boundary conditions, Meth. Appl. Anal., 18 (2011), 215-243.
doi: 10.4310/MAA.2011.v18.n2.a6. |
[8] |
J. Elschner and G. Hu, An optimization method in inverse elastic scattering for one-dimensional grating profiles, Commun. Comput. Phys., 12 (2012), 1434-1460. |
[9] |
J. Elschner and G. Hu, Elastic scattering by unbounded rough surfaces: Solvability in weighted Sobolev spaces, Appl. Anal., 94 (2015), 251-278.
doi: 10.1080/00036811.2014.887695. |
[10] |
J. Elschner, G. Schmidt and M. Yamamoto, Global uniqueness in determining rectangular periodic structures by scattering data with a single wave number, J. Inverse Ill-Posed Probl., 11 (2003), 235-244.
doi: 10.1515/156939403769237024. |
[11] |
F. Hettlich and A. Kirsch, Schiffer's theorem in inverse scattering for periodic structures, Inverse Problems, 13 (1997), 351-361.
doi: 10.1088/0266-5611/13/2/010. |
[12] |
G. Hu, Inverse wave scattering by unbounded obstacles: Uniqueness for the two-dimensional Helmholtz equation, Appl. Anal., 91 (2012), 703-717.
doi: 10.1080/00036811.2011.587811. |
[13] |
G. Hu, Y. Lu and B. Zhang, The factorization method for inverse elastic scattering from periodic structures, Inverse Problems, 29 (2013), 115005, 25pp.
doi: 10.1088/0266-5611/29/11/115005. |
[14] |
P. Grisvard, Singularités en élasticité, Arch. Rational Mech. Anal., 107 (1989), 157-180.
doi: 10.1007/BF00286498. |
[15] |
A. Kirsch, Diffraction by periodic structures, In 'Proc. Lapland Conf. Inverse Problems' (ed. L. Päivärinta et al), Springer, Berlin, Lecture Notes in Phys., 422 (1993), 87-102.
doi: 10.1007/3-540-57195-7_11. |
[16] |
C. B. Morrey, Jr. and L. Nirenberg, On the analyticity of the solutions of linear elliptic systems of partial differential equations, Communications on Pure and Applied Mathematics, 10 (1957), 271-290.
doi: 10.1002/cpa.3160100204. |
[17] |
S. Nakagawa, K. T. Nihei, L. R. Myer and E. L. Majer, Three-dimensional elastic wave scattering by a layer containing vertical periodic fractures, J. Acoust. Soc. Am., 113 (2003), 3012-3023.
doi: 10.1121/1.1572139. |
[18] |
A. Rössle, Corner singularities and regularity of weak solution for the two-dimensional Lamé equations on domains with angular corners, Journal of Elasticity, 60 (2000), 57-75.
doi: 10.1023/A:1007639413619. |
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