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Differentsial'nye Uravneniya, 2004, Volume 40, Number 9, Pages 1155–1165 (Mi de11133)  

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

Partial Differential Equations

An existence theorem for an inverse problem for a semilinear hyperbolic system

A. M. Denisov

Lomonosov Moscow State University
Abstract: In the present paper, we consider a semilinear hyperbolic system with coefficients depending on different solution components. We study the inverse problem of finding one of the coefficients on the basis of additional information on the solution. The proof of the existence theorem for the inverse problem is based on the reduction of the latter to a nonlinear operator equation, which is a nonlinear integro-differential equation for the unknown coefficient. This approach was used in [1] to prove the existence of a solution of the inverse problem for a quasilinear hyperbolic equation. Inverse problems for quasilinear hyperbolic equations and systems were also considered in [2–6] and other papers.
Received: 15.03.2004
English version:
Differential Equations, 2004, Volume 40, Issue 9, Pages 1221–1232
DOI: https://doi.org/10.1007/s10625-005-0001-0
Bibliographic databases:
Document Type: Article
UDC: 517.956.3
Language: Russian
Citation: A. M. Denisov, “An existence theorem for an inverse problem for a semilinear hyperbolic system”, Differ. Uravn., 40:9 (2004), 1155–1165; Differ. Equ., 40:9 (2004), 1221–1232
Citation in format AMSBIB
\Bibitem{Den04}
\by A.~M.~Denisov
\paper An existence theorem for an inverse problem for a semilinear hyperbolic system
\jour Differ. Uravn.
\yr 2004
\vol 40
\issue 9
\pages 1155--1165
\mathnet{http://mi.mathnet.ru/de11133}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2198525}
\transl
\jour Differ. Equ.
\yr 2004
\vol 40
\issue 9
\pages 1221--1232
\crossref{https://doi.org/10.1007/s10625-005-0001-0}
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  • https://www.mathnet.ru/eng/de11133
  • https://www.mathnet.ru/eng/de/v40/i9/p1155
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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