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About one approach to solving the inverse problem for parabolic equation. / Zhabko, Aleksei P.; Nurtazina, Karlygash B.; Provotorov, Vyacheslav V.
в: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Том 15, № 3, 01.01.2019, стр. 323-336.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - About one approach to solving the inverse problem for parabolic equation
AU - Zhabko, Aleksei P.
AU - Nurtazina, Karlygash B.
AU - Provotorov, Vyacheslav V.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Inverse problem
KW - Parabolic system
KW - The eigenvalues of boundary value problems
KW - The poles of the analytical continuation of the Green's function
UR - http://www.scopus.com/inward/record.url?scp=85074879430&partnerID=8YFLogxK
U2 - 10.21638/11702/spbu10.2019.303
DO - 10.21638/11702/spbu10.2019.303
M3 - Article
AN - SCOPUS:85074879430
VL - 15
SP - 323
EP - 336
JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ
SN - 1811-9905
IS - 3
ER -
ID: 49021807