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Inverse scattering problem for transparent obstacles

  • Vesselin Petkov (a1)

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Let K ⊂ ℝ3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K. Set

We wish to study the filtered scattering amplitude, related to the transmission problem

Here w± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω;. The function α(x) ∈ C(), called the index of refraction, has the property α(x) > 0 for x.

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(4)Georgiev, V. High frequency asymptotics of the filtered scattering amplitude for dissipative hyperbolic systems. (In preparation.)
(5)Ivrii, V.Wave fronts of solutions to boundary problems for symmetric hyperbolic systems. I. Main theorem. Sibir. Mat. Z. 20, no. 4 (1979), 741751. (In Russian.)
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(10)Majda, A. and Taylor, M.Inverse scattering problems for transparent obstacles, electro-magnetic waves and hyperbolic systems. Comm. Part. Diff. Equations 2 (1977), 395438.
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(14)Petkov, V.Propagation des singularités pour le problème de transmission et application au problème de la diffusion. C. R. Acad. Sci., Paris 290 (1980), 735755.
(15)Petkov, V.Propagation of singularities and inverse scattering problem for transparent obstacles. J. Math. Pures Appl. 60 (1982), 6590.
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Inverse scattering problem for transparent obstacles

  • Vesselin Petkov (a1)

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