Sibirskii Zhurnal Industrial'noi Matematiki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Zh. Ind. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 4, Pages 3–20 (Mi sjim800)  

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

An inverse problem of location type for a hyperbolic system

D. S. Anikonov, S. G. Kazantsev, D. S. Konovalova

Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
Full-text PDF (307 kB) Citations (1)
References:
Abstract: We consider an inverse problem for a hyperbolic system of two first-order partial differential equations with two independent variables. The right-hand sides of the system are assumed discontinuous functions. The inverse problem consists in the determination of a certain hull which contains the discontinuity line of the right-hand sides. We first study the corresponding direct problem. The existence and uniqueness of a generalized solution to the direct problem are established, and the differential properties of this solution are studied. In particular, we prove that its first-order partial derivatives are unbounded near some rays directed along characteristics. This property is the base of the algorithm for solving the inverse problem. The inverse problem is considered in the two versions: in the first version the coefficients of the equations are given, and in the second, they are unknown.
Keywords: inverse problem, hyperbolic equation, discontinuous function, generalized solution, differential property.
Received: 13.05.2013
Bibliographic databases:
Document Type: Article
UDC: 517.911.5
Language: Russian
Citation: D. S. Anikonov, S. G. Kazantsev, D. S. Konovalova, “An inverse problem of location type for a hyperbolic system”, Sib. Zh. Ind. Mat., 16:4 (2013), 3–20
Citation in format AMSBIB
\Bibitem{AniKazKon13}
\by D.~S.~Anikonov, S.~G.~Kazantsev, D.~S.~Konovalova
\paper An inverse problem of location type for a~hyperbolic system
\jour Sib. Zh. Ind. Mat.
\yr 2013
\vol 16
\issue 4
\pages 3--20
\mathnet{http://mi.mathnet.ru/sjim800}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3234788}
Linking options:
  • https://www.mathnet.ru/eng/sjim800
  • https://www.mathnet.ru/eng/sjim/v16/i4/p3
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский журнал индустриальной математики
    Statistics & downloads:
    Abstract page:418
    Full-text PDF :117
    References:89
    First page:11
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024