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Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 2, Pages 7–14 (Mi vsgu537)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

A problem on vibration of a bar with unknown boundary condition on a part of the boundary

A. B. Beylina, L. S. Pulkinab

a Samara State Technical University, 133, Molodogvardeiskaya str., Samara, 443010, Russian Federation
b Samara National Research University, 34, Moskovskoye shosse, 443086, Russian Federation

Abstract: In this paper, we study an inverse problem for hyperbolic equation. This problem arises when we consider vibration of a nonhomogeneous bar if one endpoint is fixed by spring but behavior of the other is unknown and is the subject to find. Overdetermination is given in the form of integral with respect to spacial variable. Unique solvability of this problem is proved under some conditions on data. The proof is based on a priori estimates in Sobolev space.

Keywords: hyperbolic equation, inverse problem, integral overdetermination.

Full text: PDF file (148 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file
UDC: 517.95, 624.07
Received: 05.07.2017

Citation: A. B. Beylin, L. S. Pulkina, “A problem on vibration of a bar with unknown boundary condition on a part of the boundary”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 2, 7–14

Citation in format AMSBIB
\Bibitem{BeyPul17}
\by A.~B.~Beylin, L.~S.~Pulkina
\paper A problem on vibration of a bar with unknown boundary condition on a part of the boundary
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2017
\issue 2
\pages 7--14
\mathnet{http://mi.mathnet.ru/vsgu537}
\elib{https://elibrary.ru/item.asp?id=29957946}


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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. A. V. Dyuzheva, “Nelokalnaya zadacha s dinamicheskimi granichnymi usloviyami dlya giperbolicheskogo uravneniya”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 3, 18–25  mathnet  crossref  elib
    2. A. V. Bogatov, “Zadacha s integralnym usloviem dlya odnomernogo giperbolicheskogo uravneniya”, Vestn. SamU. Estestvennonauchn. ser., 24:4 (2018), 7–12  mathnet  crossref  elib
  • Вестник Самарского государственного университета. Естественнонаучная серия
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