UTMS 2007 – 13 July 30 , 2007 Stability estimate for the hyperbolic
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چکیده
In this paper we consider the stability of the inverse problem of determining a function q(x) in a wave equation ∂ 2 t u − ∆u + q(x)u = 0 in a bounded smooth domain in R n from boundary observations. This information is enclosed in the hyperbolic (dynamic) Dirichlet-to-Neumann map associated to the solutions to the wave equation. We prove in the case of n ≥ 2 that q(x) is uniquely determined by the range restricted to a subboundary of the Dirichlet-to-Neumann map whose stability is a type of double logarithm.
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تاریخ انتشار 2007