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J. Sib. Fed. Univ. Math. Phys., 2015, Volume 8, Issue 1, Pages 38–48 (Mi jsfu404)  

This article is cited in 3 scientific papers (total in 3 papers)

On an inverse problem for quasi-linear elliptic equation

Anna Sh. Lyubanova

Institute of Space and Information Technology, Siberian Federal University, Kirenskogo, 26, Krasnoyarsk, 660026, Russia

Abstract: The identification of an unknown constant coefficient in the main term of the partial differential equation $ - kM\psi(u) + g(x) u = f(x) $ with the Dirichlet boundary condition is investigated. Here $\psi(u)$ is a nonlinear increasing function of $u$, $M$ is a linear self-adjoint elliptic operator of the second order. The coefficient $k$ is recovered on the base of additional integral boundary data. The existence and uniqueness of the solution to the inverse problem involving a function $u$ and a positive real number $k$ is proved.

Keywords: inverse problem, boundary value problem, second-order elliptic equations, existence and uniqueness theorem, filtration.

Full text: PDF file (192 kB)
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UDC: 517.95
Received: 12.11.2014
Received in revised form: 03.12.2014
Accepted: 20.12.2014
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Citation: Anna Sh. Lyubanova, “On an inverse problem for quasi-linear elliptic equation”, J. Sib. Fed. Univ. Math. Phys., 8:1 (2015), 38–48

Citation in format AMSBIB
\Bibitem{Lyu15}
\by Anna~Sh.~Lyubanova
\paper On an inverse problem for quasi-linear elliptic equation
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2015
\vol 8
\issue 1
\pages 38--48
\mathnet{http://mi.mathnet.ru/jsfu404}


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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. Sh. Lyubanova, “Obratnye zadachi dlya nelineinykh statsionarnykh uravnenii”, Matematicheskie zametki SVFU, 23:2 (2016), 65–77  mathnet  elib
    2. Anna Sh. Lyubanova, “The inverse problem for the nonlinear pseudoparabolic equation of filtration type”, Zhurn. SFU. Ser. Matem. i fiz., 10:1 (2017), 4–15  mathnet  crossref
    3. A. Sh. Lyubanova, A. V. Velisevich, “Inverse problems for the stationary and pseudoparabolic equations of diffusion”, Appl. Anal., 98:11 (2019), 1997–2010  crossref  mathscinet  zmath  isi  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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