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Matematicheskie Zametki, 1977, Volume 22, Issue 1, Pages 117–128 (Mi mzm8031)  
This article is cited in 6 scientific papers (total in 6 papers)

A positive solution of an elliptic equation with nonlinear integral boundary condition of the radiation type

A. A. Amosov

M. V. Lomonosov Moscow State University
Full-text PDF (832 kB) Citations (6)
Abstract: The problem for an elliptic equation with a nonlinear integral boundary condition describing, in particular, a stationary radiative heat transfer according to the Stefan–Boltzmann law in a system of blackbodies is considered. Theorems about the existence, uniqueness, and stability of the positive generalized solution are established.
Received: 13.07.1976
English version:
Mathematical Notes, 1977, Volume 22, Issue 1, Pages 555–561
DOI: https://doi.org/10.1007/BF01147699
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: A. A. Amosov, “A positive solution of an elliptic equation with nonlinear integral boundary condition of the radiation type”, Mat. Zametki, 22:1 (1977), 117–128; Math. Notes, 22:1 (1977), 555–561
Citation in format AMSBIB
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\by A.~A.~Amosov
\paper A~positive solution of an elliptic equation with nonlinear integral boundary condition of the radiation type
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 1
\pages 117--128
\mathnet{http://mi.mathnet.ru/mzm8031}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=466956}
\zmath{https://zbmath.org/?q=an:0355.35026}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 1
\pages 555--561
\crossref{https://doi.org/10.1007/BF01147699}
Linking options:
  • https://www.mathnet.ru/eng/mzm8031
  • https://www.mathnet.ru/eng/mzm/v22/i1/p117
    • This publication is cited in the following 6 articles:
    1. Benjámin Borsos, János Karátson, “Quasi-Newton Iterative Solution of Non-Orthotropic Elliptic Problems in 3D with Boundary Nonlinearity”, Computational Methods in Applied Mathematics, 22:2 (2022), 327  crossref
    2. Andrey Amosov, “Unique solvability of a stationary radiative–conductive heat transfer problem in a semitransparent body with absolutely black inclusions”, Z. Angew. Math. Phys., 72:3 (2021)  crossref
    3. Andrey Amosov, “Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions”, Mathematics, 9:13 (2021), 1471  crossref
    4. Andrey Amosov, “Unique solvability of a stationary radiative‐conductive heat transfer problem in a system consisting of an absolutely black body and several semitransparent bodies”, Math Methods in App Sciences, 44:13 (2021), 10703  crossref
    5. Mohamed Ghattassi, Jean Rodolphe Roche, Didier Schmitt, “Existence and uniqueness of a transient state for the coupled radiative–conductive heat transfer problem”, Computers & Mathematics with Applications, 75:11 (2018), 3918  crossref
    6. Xian-Ci Zhong, Xue-Ling Liu, Shan-Li Liao, “On a Generalized Bagley–Torvik Equation with a Fractional Integral Boundary Condition”, Int. J. Appl. Comput. Math, 3:S1 (2017), 727  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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