Diffraction by an elastic wedge with stress-free boundary: Existence and uniqueness

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 462, Issue 2065, 2006, Pages 289-317

  Kamotski, Vladimir V ^a   Lebeau, Gilles ^b  

^a University of Bath   (United Kingdom)

^b UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Clastic wedge; Diffraction; Existence; Spectral functions; Uniqueness

Indexed keywords

EID: 33846315133     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2005.1564     Document Type: Article

References (14)

1. Borovikov, V. A. 1994 Uniform stationary phase method. IEE Electromagnetic Waves Series, vol. 40. London: Institution of Electrical Engineers.
2. Budaev, B. V. & Bogy, D. B. 1996 Rayleigh wave scattering by a wedge II. Wave Motion 24, 307-314. (doi:10.1016/S0165-2125(96)00024-8)
3. Courant, R. & Hubert, D. 1902 Methods of mathematical physics. Vol. II: partial differential equations. New York: Wiley Interscience.
4. Croisille, J.-P. & Lebeau, G. 1999 Diffraction by an immersed elastic wedge. Lecture Notes in Mathematics, vol. 1723. Berlin: Springer.
5. Duvaut, G. & Lions, J. L. 1972 Les inequations en mecanique et en physique. Travaux et Recherches Mathematiques, vol. 21. Paris: Dunod.
6. Fujii, K. 1994 Rayleigh-wave scattering of various wedge corners: investigation in the wider range of wedge angles. Bull. Seismol. Soc. Am. 84, 1916-1924.
7. Gautesen, A. K. 2002 Scattering of a Rayleigh wave by an elastic three-quarter space. Wave Motion 35, 99-106. (doi:10.1016/S0165-2125(01)00085-3)
8. Kamotski, V. V., Babich, V. M., Borovikov, V. A., Fradkin, L. Ju. Submitted. On Budaev and Bogy's approach to diffraction by the traction-free elastic wedge: reduction to a singular integral problem.
9. Kondrat'ev, V. A. 1963 Boundary value problems for elliptic equations in domains with conical and angular points. Trudy Mosk. Mat. Obs. 16, 219-292.
10. Kozlov, V. A., Maz'ya, V. G. & Rossmann, J. 2001 Spectral problems associated with corner singularities of solutions to elliptic equations. Mathematical Surveys and Monographs, vol. 85. Providence, RI: American Mathematical Society.
11. Kupradze, V. D. 1965 Potential methods in the theory of elasticity. Jerusalem: Israel Program for Scientific Translations.
12. Lebeau, G. 1995 Propagation des ondes dans les diedres. Mem. Soc. Math. Fr. Nouv. Ser., no. 60.
13. 2=0. Abh. Math. Semin. Univ. Hamb. 16, 77-94.
14. Nazarov, S. A. & Plamenevski, B. A. 1994 Elliptic problems in domains with piece-wise smooth boundaries. Berlin: Walter de Gruyter.