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

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

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
Related articles on Google Scholar: Russian articles, English articles

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
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
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
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
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