Geodesic
On the dynamic inverse problem for the first-order transport system
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 153-169 Cet article a éte moissonné depuis la source Math-Net.Ru

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A dynamic inverse problem for a first-order dissipative transport system is considered for reconstructing the complex potential matrix from the dynamic response (the Dirichlet-Neumann operator) of the system for positive and negative times. In addition, a special physically motivated case of the system is considered when the potential matrix can be reconstructed only from the positive time response. 
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A. S. Mikhailov; V. S. Mikhailov. On the dynamic inverse problem for the first-order transport system. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 153-169. http://geodesic.mathdoc.fr/item/ZNSL_2024_533_a9/

[1] S. A. Avdonin, M. I. Belishev, “Boundary control and the dynamic inverse problem for a nonselfadjoint Sturm-Liouville operator”, Control and Cybernetics, 25:3 (1996), 429–440 | MR | Zbl

[2] S. A. Avdonin, V. S. Mikhaylov, “The boundary control approach to inverse spectral theory”, Inverse Problems, 26:4 (2010), 045009 | DOI | MR | Zbl

[3] M. I. Belishev, “On an approach to multidimensional inverse problems for the wave equation”, Soviet Mathematics. Doklady, 36:3 (1988), 481–484 | MR | Zbl

[4] M. I. Belishev, “The conservative model for a dissipative dynamical stystem”, J. Math. Sci., 91:2 (1998), 2711–2721 | DOI | MR

[5] M. I. Belishev, “Boundary control and inverse problems: one-dimensional variant of BC-method”, J. Math. Sci., 155:3 (2008), 343–378 | DOI | MR | Zbl

[6] M. I. Belishev, T. Sh. Khabibullin, “Data characterization in dynamical inverse problem for the 1d wave equation with matrix potential”, Zap. Nauch. Semin. POMI, 493, 2020, 48–72 | MR

[7] M. I. Belishev, V. S. Mikhaylov, “Inverse problem for one-dimensional dynamical Dirac system (BC-method)”, Inverse Problems, 30:12 (2014) | DOI | MR | Zbl

[8] M. I. Belishev, V. S. Mikhaylov, “Unified approach to classical equations of inverse problem theory”, J. Inverse and Ill-Posed Problems, 20:4 (2012), 461–488 | DOI | MR | Zbl

[9] I. Trooshin, M. Yamamoto, “Spectral properties and an inverse eigenvalue problem for non-symmetric systems of ordinary differential operators”, J. Inverse and Ill-Posed Problems, 10:6 (2003), 643–658 | DOI | MR

[10] I. Trooshin, M. Yamamoto, “Identification problem for a one-dimensional vibrating system”, Mathematical Methods in the Applied Sciences, 28:17 (2005), 2037–2059 | DOI | MR | Zbl

[11] V. S. Vladimirov, Equations of mathematical physics, Third edition, Nauka, 1976 | MR

[12] Wuqing Ning, Masahiro Yamamoto, “The Gel'fand–Levitan theory for one-dimensional hyperbolic systems with impulsive inputs”, Inverse Problems, 24:2 (2008), 025004 | DOI | MR | Zbl

[13] Wuqing Ning, Masahiro Yamamoto, “An Inverse Spectral Problem for a Nonsymmetric Differential Operator: Uniqueness and Reconstruction Formula”, Integr. Equ. Oper. Theory, 55 (2006), 273–304 | DOI | MR | Zbl

[14] Wuqing Ning, “An inverse spectral problem for a nonsymmetric differential operator: Reconstruction of eigenvalue problem”, J. Math. Anal. Appl., 327 (2007), 1396–1419 | DOI | MR | Zbl