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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2016, Volume 26, Issue 4, Pages 503–514 (Mi vuu556)  

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

MATHEMATICS

Inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions of the second kind

Ya. T. Megraliev, F. Kh. Alizade

Baku State University, ul. Z. Khalilova, 23, Baku, AZ1148, Azerbaijan

Abstract: This paper is concerned with an inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions. The definition of a classical solution of the problem is introduced. The goal of this paper is to determine the unknown coefficient and to solve the problem of interest. The problem is considered in a rectangular domain. To investigate the solvability of the inverse problem, we perform a conversion from the original problem to some auxiliary inverse problem with trivial boundary conditions. By the contraction mapping principle we prove the existence and uniqueness of solutions of the auxiliary problem. Then we make a conversion to the stated problem again and, as a result, we obtain the solvability of the inverse problem.

Keywords: inverse value problem, Boussinesq equation, existence, uniqueness, classical solution.

DOI: https://doi.org/10.20537/vm160405

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Bibliographic databases:

UDC: 517.95
MSC: 35-XX
Received: 10.10.2016

Citation: Ya. T. Megraliev, F. Kh. Alizade, “Inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions of the second kind”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:4 (2016), 503–514

Citation in format AMSBIB
\Bibitem{MegAli16}
\by Ya.~T.~Megraliev, F.~Kh.~Alizade
\paper Inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions of the second kind
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2016
\vol 26
\issue 4
\pages 503--514
\mathnet{http://mi.mathnet.ru/vuu556}
\crossref{https://doi.org/10.20537/vm160405}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3604251}
\elib{http://elibrary.ru/item.asp?id=27673736}


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    Citing articles on Google Scholar: Russian citations, English citations
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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
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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