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 Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 5, Pages 22–37 (Mi ivm8996)

An identification problem of coefficient in the special form at nonlinear lowest term for two-dimensional semilinear parabolic equation with the Cauchy data

E. N. Kriger, I. V. Frolenkov

Chair of Mathematical Analysis and Differential Equations, Siberian Federal University, 79 Svobodnyi Ave., Krasnoyarsk, 660041 Russia

Abstract: In this paper we consider the problem of identification of coefficient at nonlinear lowest term for two-dimensional semilinear parabolic equation. The sought-for coefficient depends on all variables and has the form of the sum of two functions each of them depends on time and on a spatial variable. The indicated inverse problem is reduced to non-classical direct problem which contains the traces of unknown function and its derivatives. The investigation of existence and uniqueness of solution of the auxiliary direct problem is carried out by means of the weak approximation method. We prove theorems of existence and uniqueness of the inverse problem solution in classes of smooth bounded functions. We present an example of input data satisfying the conditions of the proved theorems and corresponding solution.

Keywords: inverse problem, semilinear parabolic equation, weak approximation method, coefficient at lowest term, Cauchy problem, existence and uniqueness of solution.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:5, 17–31

UDC: 517.9

Citation: 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”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 5, 22–37; Russian Math. (Iz. VUZ), 59:5 (2015), 17–31

Citation in format AMSBIB
\Bibitem{KriFro15} \by E.~N.~Kriger, I.~V.~Frolenkov \paper An identification problem of coefficient in the special form at nonlinear lowest term for two-dimensional semilinear parabolic equation with the Cauchy data \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2015 \issue 5 \pages 22--37 \mathnet{http://mi.mathnet.ru/ivm8996} \transl \jour Russian Math. (Iz. VUZ) \yr 2015 \vol 59 \issue 5 \pages 17--31 \crossref{https://doi.org/10.3103/S1066369X15050035} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928642228} 

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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. Ekaterina N. Kriger, Igor V. Frolenkov, “An identification problem of nonlinear lowest term coefficient in the special form for two-dimensional semilinear parabolic equation”, Zhurn. SFU. Ser. Matem. i fiz., 9:2 (2016), 180–191
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