Wave scattering in a 2-D exterior domain with cuts: The Neumann problem

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 80, Issue 8, 2000, Pages 535-546

  Krutitskii, P A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044522733     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/1521-4001(200008)80:8<535::AID-ZAMM535>3.0.CO;2-1     Document Type: Article

References (22)

1. ARSENIN, V. Ya.: Methods of mathematical physics. Nauka, Moscow 1974 (Russian).
2. GAKHOV, F. D.: Boundary value problems. Pergamon Press, Oxford; Addison-Wesley, Reading, Mass., 1966.
3. KRUTITSKII, P. A.: Dirichlet problem for the Helmholtz equation outside cuts in a plane. Comput. Math. Math. Phys. 34 (1994) 8/9, 1073-1090
4. (Transl. from Zhurn. Vych. Mat. Mat. Fiz. 34 (1994) 8/9, 1237-1258 (Russian)).
5. KRUTITSKII, P. A.: Neumann problem for the Helmholtz equation outside cuts in a plane. Comput. Math. Math. Phys. 34 (1994) 11, 1421-1431
6. (Transl. from Zhurn. Vych. Mat. Mat. Fiz. 34 (1994) 11, 1652-1665 (Russian)).
7. MUSKHELISHVILI, N. I.: Singular integral equations. Noordhoff, Groningen 1953, reprinted 1972.
8. KRUTITISKII, P. A.: Wave propagation in a 2-D external domain bounded by closed and open curves. Nonlinear Analysis, TMA 32 (1998), 135-144.
9. KRUTITSKII, P. A.: The Dirichlet problem for the 2-D Helmholtz equation in a multiply connected domain with cuts. ZAMM 77 (1997) 12, 883-890.
10. KRUTITSKII, P. A.: The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves. Internat. J. Math. Math. Sci. 21 (1998) 2, 209-216.
11. KRUTITSKII, P. A.: The Neumann problem on wave propagation in a 2-D external domain with cuts. J. Math. Kyoto Univ. 38 (1998) 3, 439-452.
12. NIKIFOROV, A. F.; UVAROV, V. B.: Special functions of mathematical physics. Birkhäuser, Basel 1998.
13. COLTON, D.; KRESS, R.: Integral equation methods in scattering theory. John Wiley & Sons, New York 1983.
14. VLADIMIROV, V. S.: Equations of mathematical physics. Marcel Dekker, NY 1971.
15. HÖRMANDER, L.: Linear partial differential operators. Springer, Berlin 1963.
16. BELOTSERKOVSKY, S. M.; LIFANOV, I. K.: Method of discrete vortices. CRC Press, New York 1993.
17. LIFANOV, I. K.: Singular integral equations and discrete vortices. VSP, Zeist 1996.
18. NISHIMURA, N.: Crack determination problems. Theor. Appl. Mech. 46 (1997), 39-57.
19. NISHIMURA, N. A.: A numerical method on crack determination by the boundary integral equation method. In: TIKHONOV, A. N. (ed.): Ill-posed problems in natural science. VSP/TVP 1992, pp. 553-562.
20. NISHIMURA, N.; KOBAYASHI, S.: A boundary integral equation method for an inverse problem related to crack detection. Internat. J. Numer. Meth. Engin. 32 (1991), 1371-1387.
21. NISHIMURA, N.; KOBAYASHI, S.: Determination of cracks having arbitrary shapes with the boundary integral equation method. Engin. Anal. Boundary Elements 15 (1995), 180-195.
22. KRUTITSKII, P. A.: Method of interior boundaries in a mixed problem of acoustic scattering. Math. Probl. Engin. 5 (1999), 173-192.