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Sib. Zh. Ind. Mat., 2012, Volume 15, Number 2, Pages 139–146 (Mi sjim733)  

This article is cited in 4 scientific papers (total in 4 papers)

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

I. V. Frolenkov, G. V. Romanenko

Siberian Federal University, Krasnoyarsk, Russia

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.

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Bibliographic databases:
UDC: 517.9
Received: 04.08.2011

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://www.ams.org/mathscinet-getitem?mr=3099842}


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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. 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
    2. 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
    3. 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
    4. 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
  • Сибирский журнал индустриальной математики
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