
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. Akhtyamov^{ab}, V. A. Sadovnichy^{c}, Ya. T. Sultanaev^{b} ^{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
Abstract:
For the inverse problem of reconstructing the nonselfadjoint 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 selfadjoint 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 selfadjoint diffusion operator one can use even less spectral data as compared with the reconstruction of a selfadjoint 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.
Funding Agency 
Grant Number 
Russian Foundation for Basic Research 
150101095_a 1741020195_r_a 1741020230_r_a 
This work was supported by the Russian Foundation for Basic Research and by the Academy of Sciences of the Republic of Bashkortostan (projects No. 150101095 a, 1741020195r a, 1741020230r a). 
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MSC: 34A55, 34B05, 58C40 Received: 12.08.2016
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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
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\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.
\yr 2017
\vol 8
\issue 1
\pages 1022
\mathnet{http://mi.mathnet.ru/emj244}
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A. M. Akhtyamov, Kh. R. Mamedov, E. N. Yilmazoglu, “Boundary inverse problem for starshaped graph with different densities stringsedges”, 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 fourthorder differential operator with nonseparated boundary conditions”, Differ. Equ., 54:10 (2018), 1354–1362

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