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Chelyab. Fiz.-Mat. Zh., 2018, Volume 3, Issue 2, Pages 153–171 (Mi chfmj96)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Linear inverse problems for a class of equations of Sobolev type

A. I. Kozhanovab, G. V. Namsaraevac

a Sobolev Institute of Mathematics of SB RAS, Novosibirsk, Russia
b Novosibirsk State University (National Research University), Novosibirsk, Russia
c East Siberia State University of Technology and Management, Ulan-Ude, Russia

Abstract: We study the solvability of inverse problems of finding together with the solution $u(x,t)$ also an unknown factor $q(t)$ in equation
$$D^{2p}_t(u-\Delta u)+Bu=f_0(x,t)+q(t)h_0(x,t)$$
($t\in (0,T)$, $x\in\Omega\subset \mathbb{R}^n$, $p$ is a natural number, $D^k_t=\frac{\partial^k}{\partial t^k}$, $\Delta$ is the Laplace operator with respect to the spatial variables, $B$ is a linear second-order differential operator, acting also on the spatial variables, $f_0(x,t)$ and $h_0(x,t)$ are given functions). Integral overdetermination condition is used as an additional condition in these problems. The existence and uniqueness theorems for regular solutions (i. e. having all the generalized derivatives in the sense of S.L. Sobolev, presenting in the equation) are proved.

Keywords: Sobolev type equation, inverse problem, unknown right-hand side, integral overdetermination, regular solution, solution existence, solution uniqueness.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00620


DOI: https://doi.org/10.24411/2500-0101-2018-13203

Full text: PDF file (765 kB)
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UDC: 517.95
Received: 12.04.2018
Revised: 03.05.2018

Citation: A. I. Kozhanov, G. V. Namsaraeva, “Linear inverse problems for a class of equations of Sobolev type”, Chelyab. Fiz.-Mat. Zh., 3:2 (2018), 153–171

Citation in format AMSBIB
\Bibitem{KozNam18}
\by A.~I.~Kozhanov, G.~V.~Namsaraeva
\paper Linear inverse problems for a class of equations of Sobolev type
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2018
\vol 3
\issue 2
\pages 153--171
\mathnet{http://mi.mathnet.ru/chfmj96}
\crossref{https://doi.org/10.24411/2500-0101-2018-13203}


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    This publication is cited in the following articles:
    1. Ya. T. Megraliev, B. K. Velieva, “Obratnaya kraevaya zadacha dlya linearizovannogo uravneniya Benni-Lyuka s nelokalnymi usloviyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:2 (2019), 166–182  mathnet  crossref  elib
  • Chelyabinskiy Fiziko-Matematicheskiy Zhurnal
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