Abstract
An approach to the inverse problem (the so-called BC-method) based on boundary-control theory is developed. A procedure of reconstructing a nonsymmetric matrix-function (a potential) given on a semiaxis by a dynamical response operator is described. The results of numerical tests are presented. Bibliography: 6 titles.
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References
M. I. Belishev, “On an approach to multidimensional inverse problems for the wave equation,”Dokl. Akad. Nauk SSSR,297, No. 3, 524–527 (1987).
S. A. Avdonin, M. I. Belishev, and S. A. Ivanov, “Boundary-control and matrix inverse problems for the equationu tt−u xx+V(x)u=0”,Mat. Sb.,182, No. 3, 303–331 (1991).
A. S. Blagoveshchenskii, “The non-self-adjoint inverse boundary-value problem in matrix form for the hyperbolic differential equation,”Probl. Mat. Fiz., No. 5, 38–61 (1971).
I. Ts. Gokhberg and M. G. Krein,The Theory of Volterra Operations in Hilbert Spaces and Its Applications [in Russian], Nauka, Moscow (1967).
S. Avdonin and M. Belishev, “Boundary control and the dynamical inverse problem for a nonselfadjoint Sturm-Liouville operator,”Control Cybernetics,25, No. 3, 429–440 (1996).
M. I. Belishev, “On the uniqueness of the reconstruction of lowest terms of the wave equation by dynamical boundary data,”Zap. Nauchn. Semin. POMI,249, 55–76 (1997).
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 7–21.
Translated by T. N. Surkova.
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Avdonin, S.A., Belishev, M.I. & Rozhkov, Y.S. The dynamical inverse problem for a non-self-adjoint sturm-liouville operator. J Math Sci 102, 4139–4148 (2000). https://doi.org/10.1007/BF02673844
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DOI: https://doi.org/10.1007/BF02673844