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On the unique solvability of a class of modified boundary integral equations

Published online by Cambridge University Press:  20 January 2009

R. E. Kleinman  and
G. F. Roach
R. E. Kleinman
Affiliation:
University of Delaware
G. F. Roach
Affiliation:
University of Strathclyde
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In a recent paper the authors considered the transmission problem for the Helmholtz equation by using a reformulation of the problem in terms of a pair of coupled boundary integral equations with modified Green's functions as kernels. In this note we settle the question of the unique solvability of these modified boundary integral equations.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 3 , October 1984 , pp. 303 - 311
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Angell, T. S. and Kleinman, R. E.Modified Green's functions and the third boundary value problem for the Helmholtz equation, J. Math. Anal, and Applic. 97 (1983), 81–94.CrossRefGoogle Scholar
2.Colton, D. L. and Kress, R.Integral Equation Methods in Scattering Theory (John Wiley, New York, 1983).Google Scholar
3.Jones, D. S.Integral equations for the exterior acoustic problem, Q. Jour. Mech. App. Math. 27 (1974), 129–142.CrossRefGoogle Scholar
4.Kittappa, R. and Kleinman, R. E.Acoustic scattering by penetrable homogeneous objects, J. Maths. Phys. 16 (1975), 421–432.CrossRefGoogle Scholar
5.Kleinman, R. E. and Kress, R.On the condition number of integral equations in acoustics using modified fundamental solutions, IMA J. App. Maths. 31 (1983), 79–90.CrossRefGoogle Scholar
6.Kleinman, R. E. and Roach, G. F.On modified Green's functions in exterior problems for the Helmholtz equation, Proc. Roy. Soc. London A383 (1982), 313–332.Google Scholar
7.Kleinman, R. E. and Roach, G. F.Operators of minimal norm via modified Green's functions, Proc. Roy. Soc. Edinburgh 74A (1983), 163–178.CrossRefGoogle Scholar
8.Kleinman, R. E. and Roach, G. F.New integral equations for scattering by penetrable objects, Proc. URSI Symposium on Electromagnetic Theory, Santiago de Compostela, Spain, 1983, 131–133.Google Scholar
9.Kleinman, R. E. and Roach, G. F.Modified Green's functions for the Transmission problem,Proceedings of Conference on Classical Scattering Theory, 1983 (Shiva, to appear).Google Scholar
10.Kleinman, R. E. and Roach, G. F. New integral equations for scattering by penetrable bodies II, Radio Science, to appear.Google Scholar
11.Kleinman, R. E., Roach, G. F. and Ström, S. E. G.The Null Field Method and modified Green's functions, Proc. Roy. Soc. London A394 (1984), 121–136.Google Scholar
12.Kress, R. and Roach, G. F.Transmission problems for the Helmholtz equation, J. Maths. Phys. 19 (1978), 1433–1437.CrossRefGoogle Scholar
13.Millar, R. F.The Rayleigh hypothesis and a related least squares solution to scattering problems for periodic surfaces and other scatters, Radio Science 8 (1973), 785–796.CrossRefGoogle Scholar
14.Ursell, F.On the exterior problems of acoustics II, Math. Proc. Comb. Phil. Soc. 84 (1978), 545–548CrossRefGoogle Scholar