Geodesic
About one approach to solving the inverse problem for parabolic equation
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 3, pp. 323-336

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Consider the problem of determining the coefficients in the differential equation of parabolic types and boundary conditions on the known sections of the solutions of the initial-boundary value problem. Used spectral approach based on spectral properties of the elliptic operator of the initial-boundary value problem and the methods of solving the inverse spectral problem of restoring the Sturm–Liouville operator on two sequences of the eigenvalues, that corresponding to two sets of boundary conditions. In the work presented sufficient conditions of determination of two sequences of the eigenvalues by two sets of boundary conditions and terms of the uniqueness of the solution of the inverse problem The paper considers the case where the initial-boundary value problem contains the specifics — the interval of change contains variable include a finite number of the points, where the differential equation is meaningless and replaced conditions agreement.
Keywords: parabolic system, inverse problem, the eigenvalues of boundary value problems, the poles of the analytical continuation of the Green's function. 
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     title = {About one approach to solving the inverse problem for parabolic equation},
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A. P. Zhabko; K. B. Nurtazina; V. V. Provotorov. About one approach to solving the inverse problem for parabolic equation. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 3, pp. 323-336. http://geodesic.mathdoc.fr/item/VSPUI_2019_15_3_a2/