This article is cited in 3 scientific papers (total in 3 papers)
Inverse problem for the diffusion operator with symmetric functions and general boundary conditions
A. M. Akhtyamovab, V. A. Sadovnichyc, Ya. T. Sultanaevb
a Bashkir State University, ul. Frunze 32, 450074 Ufa, Russia
b Mavlutov Institute of Mechanics, Russian Academy of Sciences,
71 Oktyabrya Pr, 450054 Ufa, Russia
c M.V. Lomonosov Moscow State University, Leninskie gory,
119992 Moscow, Russia
For the inverse problem of reconstructing the nonself-adjoint diffusion operator with symmetric functions and general boundary conditions a uniqueness theorem is proved. As spectral data only one spectrum and six eigenvalues are used. Earlier this inverse problem was not considered. The inverse problem of reconstructing the self-adjoint diffusion operator with nonseparated boundary conditions was considered. To uniquely reconstruct this operator two spectra, some sequence of signs, and some complex number were used as spectral data. We show that in the symmetric case to uniquely reconstruct the self-adjoint diffusion operator one can use even less spectral data as compared with the reconstruction of a self-adjoint problem in earlier papers; more precisely, we need one spectrum and, in addition, five eigenvalues. The special cases of these general inverse problems are considered too. In these special cases less spectral data are used. Algorithms of reconstructing diffusion operator are given. Moreover, we show that results obtained in the present paper generalize the results for the inverse problem of reconstructing the diffusion operator with separated boundary conditions.
Keywords and phrases:
inverse eigenvalue problem, diffusion operator, nonseparated boundary conditions.
|Russian Foundation for Basic Research
|This work was supported by the Russian Foundation for Basic Research and by the Academy of Sciences of the Republic of Bashkortostan (projects No. 15-01-01095 a, 17-41-020195-r a, 17-41-020230-r a).
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MSC: 34A55, 34B05, 58C40
A. M. Akhtyamov, V. A. Sadovnichy, Ya. T. Sultanaev, “Inverse problem for the diffusion operator with symmetric functions and general boundary conditions”, Eurasian Math. J., 8:1 (2017), 10–22
Citation in format AMSBIB
\by A.~M.~Akhtyamov, V.~A.~Sadovnichy, Ya.~T.~Sultanaev
\paper Inverse problem for the diffusion operator with symmetric functions and general boundary conditions
\jour Eurasian Math. J.
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A. M. Akhtyamov, Kh. R. Mamedov, E. N. Yilmazoglu, “Boundary inverse problem for star-shaped graph with different densities strings-edges”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:3 (2018), 5–17
V. A. Sadovnichii, Ya. T. Sultanaev, A. M. Akhtyamov, “Inverse problem for a differential operator with nonseparated boundary conditions”, Dokl. Math., 97:2 (2018), 181–183
V. A. Sadovnichii, Ya. T. Sultanaev, A. M. Akhtyamov, “Inverse problem for a fourth-order differential operator with nonseparated boundary conditions”, Differ. Equ., 54:10 (2018), 1354–1362
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