Loading [MathJax]/jax/output/SVG/config.js
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, 2012, Volume 15, Number 2, Pages 139–146 (Mi sjim733)  
This article is cited in 5 scientific papers (total in 5 papers)

On the solution of an inverse problem for a multidimensional parabolic equation

I. V. Frolenkov, G. V. Romanenko

Siberian Federal University, Krasnoyarsk, Russia
Full-text PDF (207 kB) Citations (5)
References:
PDF
HTML
Abstract: We study the inverse problem for a multidimensional parabolic equation with an unknown coefficient at the differential operator of second order with respect to a chosen variable with the Cauchy data. The initial condition has a special form and is given in the form of the scalar product of two vector-valued functions that depend on different variables. We obtain sufficient conditions for the existence and uniqueness of the solution to an auxiliary direct problem and the initial inverse problem. We use the weak approximation method for the proof.
Keywords: inverse problem, approximation, weak approximation method, theorem of existence and uniqueness, partial differential equations, parabolic equation.
Received: 04.08.2011
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: I. V. Frolenkov, G. V. Romanenko, “On the solution of an inverse problem for a multidimensional parabolic equation”, Sib. Zh. Ind. Mat., 15:2 (2012), 139–146
Citation in format AMSBIB
\Bibitem{FroRom12}
\by I.~V.~Frolenkov, G.~V.~Romanenko
\paper On the solution of an inverse problem for a~multidimensional parabolic equation
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 2
\pages 139--146
\mathnet{http://mi.mathnet.ru/sjim733}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3099842}
Linking options:
  • https://www.mathnet.ru/eng/sjim733
  • https://www.mathnet.ru/eng/sjim/v15/i2/p139
    • This publication is cited in the following 5 articles:
    1. S. G. Pyatkov, O. A. Soldatov, “On some classes of inverse parabolic problems of recovering the thermophysical parameters”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 15:3 (2023), 23–33  mathnet  crossref
    2. E. N. Kriger, I. V. Frolenkov, “An identification problem of coefficient in the special form at nonlinear lowest term for two-dimensional semilinear parabolic equation with the Cauchy data”, Russian Math. (Iz. VUZ), 59:5 (2015), 17–31  mathnet  crossref
    3. Galina V. Romanenko, “A representation of solution of the identification problem of the coefficients at second order operator in the multi-dimensional parabolic equations system”, Zhurn. SFU. Ser. Matem. i fiz., 7:1 (2014), 100–111  mathnet
    4. I. V. Frolenkov, G. V. Romanenko, “On the solvability of special systems of one-dimensional loaded parabolic equations and composite-type systems with Cauchy data”, J. Appl. Industr. Math., 8:2 (2014), 196–207  mathnet  crossref  mathscinet
    5. Igor V. Frolenkov, Ekaterina N. Kriger, “An identification problem of coefficient in the special form at source function for multi-dimensional parabolic equation with Cauchy data”, Zhurn. SFU. Ser. Matem. i fiz., 6:2 (2013), 186–199  mathnet
    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:453
    Full-text PDF :151
    References:89
    First page:9
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025