Geodesic
Determination of a wave field in a laterally inhomogeneous medium from boundary data
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 55-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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We deal with the Cauchy problem for a perturbed wave equation in the half-plane with data given on a part of the space-time boundary. The equation in consideration describes a wave process in a laterally inhomogeneous medium. We propose a reconstruction algorithm, which is applicable to the problem of determining nonstationary wave field from boundary data arising in geophysics. 
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     title = {Determination of a wave field in a laterally inhomogeneous medium from boundary data},
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}
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M. N. Demchenko. Determination of a wave field in a laterally inhomogeneous medium from boundary data. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 55-68. http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a3/

[1] M. M. Lavrentev, V. G. Romanov, S. P. Shishatskii, Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980 | MR

[2] V. Isakov, Inverse Problems for Partial Differential Equations, Appl. Math. Sci., 127, 2nd Edition, Springer, 2006 | MR | Zbl

[3] D. Tataru, “Unique Continuation for Solutions to PDE's; Between Hörmander's Theorem and Holmgren's Theorem”, Communications in Partial Differential Equations, 20:5–6 (1995), 855–884 | MR | Zbl

[4] R. Kurant, D. Gilbert, Metody matematicheskoi fiziki, v. II, Uravneniya s chastnymi proizvodnymi, Mir, M., 1964

[5] M. N. Demchenko, “Reconstruction of solution to the wave equation from Cauchy data on the boundary”, Proceedings of the International Conference Days on Diffraction, 2018, 66–70

[6] M. N. Demchenko, “O zadache Koshi dlya volnovogo uravneniya s dannymi na granitse”, Zap. nauchn. semin. POMI, 471, 2018, 99–112

[7] A. S. Blagoveshchensky, F. N. Podymaka, “On a Cauchy problem for the wave equation with data on a time-like hyperplane”, Proceedings of the International Conference Days on Diffraction, 2016, 31–34

[8] S. I. Kabanikhin, D. B. Nurseitov, M. A. Shishlenin, B. B. Sholpanbaev, “Inverse problems for the ground penetrating radar”, J. Inverse Ill-Posed Probl., 21 (2013), 885–892 | MR | Zbl

[9] F. Natterer, “Photo-acoustic inversion in convex domains”, Inverse Probl. Imaging, 6:2 (2012), 1–6 | DOI | MR

[10] T. A. Voronina, V. A. Tcheverda, V. V. Voronin, “Some properties of the inverse operator for a tsunami source recovery”, Siberian Electronic Mathematical Reports, 11 (2014), 532–547 | MR | Zbl

[11] M. I. Belishev, “Recent progress in the boundary control method”, Inverse problems, 23:5 (2007), R1–R67 | DOI | MR | Zbl

[12] L. D. Faddeev, “Obratnaya zadacha kvantovoi teorii rasseyaniya. II”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat., 3, VINITI, M., 1974, 93–180

[13] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967