The inverse scattering problem for the acoustic equation in a half-space

Author: Karamyan G.

Source: Inverse Problems, Volume 18, Number 6, 2002 , pp. 1673-1686(14)

Publisher: Institute of Physics Publishing

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Abstract:

In this paper we consider the acoustic equation c2 (x)u + k2u 0, x+n, n 3, where 0 < c1c2 (x) c2, c(x) - 1 O(e-|x|), > 0 and +n {(x', xn) n : xn 0}. This equation can be rewritten in the form -u - k2u + q(x)u 0, where q(x) k2 (1 - c-2 (x)) O(e-|x|). Assuming that u(x) satisfies Robin boundary conditions on xn 0, we prove that the scattering amplitude at fixed energy determines the potential function q(x).

Language: English

Document Type: Miscellaneous

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