The oblique derivative problem for the Helmholtz equation and scattering tidal waves

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

Volumn 457, Issue 2011, 2001, Pages 1735-1755

  Krutitskii, P A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Helmholtz equation; Oblique derivative problem; Thin bodies; Tidal waves

Indexed keywords

EID: 57249097744     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2001.0787     Document Type: Article

References (35)

1. Colton, D. & Kress, R. 1983 Integral equation methods in scattering theory. Wiley.
2. Crease, J. 1956 Long waves on a rotating Earth in the presence of a semi-infinite barrier. J. Fluid Mech. 1, 86-96.
3. Crease, J. 1958 The propagation of long waves into a channel in a rotating system. J. Fluid Mech. 4, 306-320.
4. Davydov, A. G., Zakharov, Ye. V. & Pimenov, Yu. V. 1981 A method of solving problems of the diffraction of electromagnetic waves by infinitely thin cylindrical screens. Dokl. Akad. Nauk SSSR 261, 338-341. (In Russian.)
5. Durand, M. 1983 Layer potentials and boundary value problems for the Helmholtz equation in the complement of a thin obstacle. Math. Meth. Appl. Sci. 5, 389-421.
6. Gabov, S. A. 1977 An angular potential and its applications. Math. USSR Sbornik 32, 423-436.
7. Gakhov, F. D. 1966 Boundary value problems. Oxford: Pergamon.
8. Grisvard, P. 1985 Elliptic problems in nonsmooth domains, ch. 3, § 3.24. Boston, MA: Pitman.
9. Jeffreys, H. 1924 The free oscillations of water in an elliptic lake. Proc. Lond. Math. Soc. 23, 455-476.
10. Krutitskii, P. A. 1991 On an application of S. A. Gabov's potentials in the physics of semiconductors. USSR Comp. Maths Math. Phys. 31, 75-84.
11. Krutitskii, P. A. 1994a Dirichlet problem for the Helmholtz equation outside cuts in a plane. Comp. Maths Math. Phys. 34, 1073-1090.
12. Krutitskii, P. A. 1994& Neumann problem for the Helmholtz equation outside cuts in a plane. Comp. Maths Math. Phys. 34, 1421-1431.
13. Krutitskii, P. A. 1996a The mixed problem for the Helmholtz equation in a multiply connected domain. Comp. Maths Math. Phys. 36, 1087-1095.
14. Krutitskii, P. A. 1996& Fast stratified flow over several obstacles, including wings. IMA J. Appl. Math. 57, 243-256.
15. Krutitskii, P. A. 1996c Wave propagation in a two-dimensional external domain with cuts. Applicable Analysis 62, 297-309.
16. Krutitskii, P. A. 1998 On the electric current from electrodes in a magnetized semiconductor film. IMA J. Appl. Math. 60, 285-297.
17. Krutitskii, P. A. 2000 Wave scattering in a two-dimensional exterior domain with cuts: the Neumann problem. Z. Angew. Math. Mech. 80, 535-546.
18. Lamb, H. 1932 Hydrodynamics, ch. 8, § 207. Cambridge University Press.
19. LeBlond, P. H. & Mysak, L. A. 1978 Waves in the ocean, p. 267. Elsevier.
20. Lifanov, I. K. 1996 Singular integral equations and discrete vortices. Zeist: VSP.
21. Muskhelishvili, N. I. 1972 Singular integral equations. Groningen: Noordhoff.
22. Nikiforov, A. F. & Uvarov, V. B. 1988 Special functions of mathematical physics. Basel: Birkhäuser.
23. Noble, B. 1958 Methods based on the Wiener-Hopf technique. Pergamon.
24. Povzner, A. Ya. & Suharevsky, I. V. 1959 Integral equations of 2nd kind for problems of diffraction by screens. Dokl. Akad. Nauk SSSR 127, 291-294. (In Russian.)
25. Proudman, J. 1915 Diffraction of tidal waves on flat rotating sheet of water. Proc. Lond. Math. Soc. 14, 89-102.
26. Proudman, J. 1953 Dynamical oceanography, p. 220. London: Methuen.
27. Santos, A. M. & Speck, F.-O. 1996 Sommerfeld diffraction problems with oblique derivative. Department de Matematica, Instituto Superior Tecnico de Lisboa. Preprint 7/96, March 1996.
28. Sekerzh-Zenkovich, S. Ya. 1968 Diffraction of plane waves by a circular island. Fiz. Atmos. i Ocean. 4, 69-79. (In Russian.)
29. Sretensky, L. N. 1936 Theory of wave motions of a fluid, ch. 5. Moscow: ONTI. (In Russian.)
30. Sretensky, L. N. 1987 Dynamical theory of tides, ch. 1. Moscow: Nauka. (In Russian.)
31. Tuchkin, Yu. A. 1987 Scattering of waves by an unclosed cylindrical screen of an arbitrary profile with Neumann boundary condition. Dokl. Akad. Nauk SSSR 293, 343-345. (In Russian.)
32. Tuchkin, Yu. A. & Shestopalov, V. P. 1985 Scattering of waves by a finite system of cylindrical screens of arbitrary profile with Dirichlet boundary condition. Dokl. Akad. Nauk SSSR 285, 1107-1109. (In Russian.)
33. Vladimirov, V. S. 1971 Equations of mathematical physics. New York: Dekker.
34. Wolfe, P. 1969 An existence theorem for the reduced wave equation. Proc. Am. Math. Soc. 21, 663-666.
35. Zakharov, Ye. V. & Sobyanina, I. V. 1986 One-dimensional integro-differential equations of problems of diffraction by screens. Zh. Vychisl. Matem. Mat. Fiz. 26, 632-636. (In Russian.)