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A stable method for an inverse problem in acoustic scattering by an obstacle with an impedance boundary condition

Published online by Cambridge University Press:  14 November 2011

Robert T. Smith
Robert T. Smith
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia24061, U.S.A.
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Synopsis

We examine the case of plane, time-harmonic acoustic waves in two dimensions, scattered by an obstacle on the surface of which an impedance boundary condition is imposed. A stable method is developed for solving the inverse problem ofdetermining both the shape of the scatterer and the surface impedance from measurements of the asymptotic behaviour of the scattered waves at low frequencies. We accomplish this by minimizing an appropriate functional over a compact set of admissible boundary curves and admissible impedances.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 98 , Issue 3-4 , 1984 , pp. 355 - 364
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Colton, D. L.. The inverse scattering problem for time-harmonic acoustic waves. SIAM Rev. 26 (1984), 323–350.CrossRefGoogle Scholar
2Colton, D. L. and Kirsch, A.. Stable methods for solving the inverse scattering problem for a cylinder. Proc. Roy. Soc. Edinburgh Sect. A 89 (1981), 181–188.CrossRefGoogle Scholar
3Colton, D. L. and Kress, R.. Integral Equation Methods in Scattering Theory (New York: John Wiley, 1983).Google Scholar
4Courant, R. and Hilbert, D.. Methods of Mathematical Physics, Vol. II (New York: Interscience, 1961).Google Scholar
5Kleinman, R. E.. Some applications of functional analysis in classical scattering. In Mathematical Methods and Applications of Scattering Theory (ed. Santo, J. A. De et al. )(Berlin: Springer, 1980).Google Scholar
6Lax, P. and Phillips, R.. Scattering Theory (New York: Academic Press, 1967).Google Scholar
7Smith, R. T.. An inverse acoustic scattering problem for an obstacle with an impedance boundary condition. J. Math. Anal. AppL, to appear.Google Scholar
8Smith, R. T.. Stable methods for an inverse problem in acoustic scattering by an obstacle and an inhomogeneous medium. Math. Methods AppL Sci., to appear.Google Scholar
9Watson, G. N.. A Treatise on the Theory of Bessel Functions (Cambridge: Cambridge Univ. Press, 1944).Google Scholar