Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on an inverse scattering problem


Authors: John F. Ahner and Charles S. Kahane
Journal: Proc. Amer. Math. Soc. 73 (1979), 88-91
MSC: Primary 35R30; Secondary 35P25, 78A45
MathSciNet review: 512064
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Abstract: Here it is shown that the inverse scattering problem of a plane wave incident off a spherically symmetric medium is an improperly posed problem and that if a continuous index of refraction exists, then it is unique.


References [Enhancements On Off] (What's this?)

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  • [2] David Colton, The scattering of acoustic waves by a spherically stratified inhomogeneous medium, Proc. Roy. Soc. Edinburgh Sect. A 76 (1977), no. 4, 345–350. MR 0462119
  • [3] R. E. Kleinman, The Dirichlet problem for the Helmholtz equation, Arch. Rational Mech. Anal. 18 (1965), 205–229. MR 0172602
  • [4] Chris Rorres, Low energy scattering by an inhomogeneous medium and by a potential., Arch. Rational Mech. Anal. 39 (1970), 340–357. MR 0270637
  • [5] Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0512064-4
Keywords: Inverse scattering, improperly posed problems
Article copyright: © Copyright 1979 American Mathematical Society