On some inverse coefficient problems with the pointwise overdetermination for mathematical models of filtration

S.N. Shergin1, E.I. Safonov1, S.G. Pyatkov1,2 1Ugra State University, Khanty-Mansyisk, Russian Federation 2South Ural State University, Chelyabinsk, Russian Federation E-mails: S_pyatkov@ugrasu.ru, Ssn@ugrasu.ru, dc.gerz.hd@gmail.com Сергей Николаевич Шергин, аспирант, ведущий программист, отдел по...

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Bibliographic Details
Published in:Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software"
Main Authors: Shergin, S.N., Safonov, E.I., Pyatkov, S.G., Шергин, С.Н., Сафонов, Е.И., Пятков, С.Г.
Format: Article in Journal/Newspaper
Language:English
Published: Издательский центр ЮУрГУ 2019
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Online Access:http://dspace.susu.ru/xmlui/handle/0001.74/40182
https://doi.org/10.14529/mmp190107
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Summary:S.N. Shergin1, E.I. Safonov1, S.G. Pyatkov1,2 1Ugra State University, Khanty-Mansyisk, Russian Federation 2South Ural State University, Chelyabinsk, Russian Federation E-mails: S_pyatkov@ugrasu.ru, Ssn@ugrasu.ru, dc.gerz.hd@gmail.com Сергей Николаевич Шергин, аспирант, ведущий программист, отдел по набору и профориентационной работе, Югорский государственный университет (г. Ханты- Мансийск, Российская Федерация), ssn@ugrasu.ru. Егор Иванович Сафонов, кандидат физико-математических наук, доцент, Высшая цифровая школа, Югорский государственный университет (г. Ханты-Мансийск, Российская Федерация), dc.gerz.hd@gmail.com. Сергей Григорвевич Пятков, доктор физико-математических наук, профессор, заведующий кафедрой «Высшая математика:», Югорский государственный университет (г. Ханты-Мансийск, Российская Федерация); научно- исследователвская лаборатория «Неклассические уравнений математической физики», Южно-Уралвский государственный университет (г. Челябинск, Российская Федерация), S_pyatkov@ugrasu.ru We examine inverse problems of recovering coefficients in a linear pseudoparabolic equation arising in the filtration theory. Boundary conditions of the Neumann type are supplemented with the overtermination conditions which are the values of the solution at some interior points of a domain. We expose existence and uniqueness theorems in the Sobolev spaces. The solution is regular, i. e., it possesses all generalized derivatives occurring in the equation containing in some Lebesgue space. The method of the proof is constructive. The problem is reduced to a nonlinear operator equation with a contraction operator whenever the time interval is sufficiently small. Involving the method of the proof, we construct a numerical algorithm, the corresponding software bundle, and describe the results of numerical experiments in the two-dimensional case in the space variables. The unknowns are a solution to the equation and the piezo-conductivity coefficient of a fissured rock. The main method of numerical solving the problem is the ...