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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 2(35), Pages 39–49 (Mi vsgtu1306)  

This article is cited in 3 scientific papers (total in 3 papers)

Differential Equations

A Double Inverse Problem for Fredholm Integro-Differential Equation of Elliptic Type

T. K. Yuldashev

M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, 660014, Russian Federation

Abstract: In this paper the double inverse problem for partial differential equations is considered. The method of studying the one value solvability of the double inverse problem for a Fredholm integro-differential equation of elliptic type with degenerate kernel is offered. First the method of degenerate kernel designed for Fredholm integral equations is modified and developed to the case of Fredholm integro-differential equation of elliptic type. The system of differential-algebraic equations is obtained. The inverse problem is called double inverse problem if the problem consisted to restore the two unknown functions by the aid of given additional conditions. The first restore function is nonlinear with respect to the second restore function. In solving the inverse problem with respect to the first restore function the inhomogeneous differential equation of the second order is obtained, which is solved by the method of variation of arbitrary constants with initial value conditions. With respect to the second restore function the nonlinear integral equation of the first kind is obtained, which is reduced by the aid of special nonclassical integral transform into nonlinear Volterra integral equation of the second kind. Further the method of successive approximations is used, combined with the method of compressing maps.

Keywords: double inverse problem, elliptic type equation, Fredholm equation with degenerate kernel, inhomogeneous differential equation, one valued solvability

DOI: https://doi.org/10.14498/vsgtu1306

Full text: PDF file (606 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.968.21
MSC: 45K05, 45Q05, 45B05
Original article submitted 15/IV/2014
revision submitted – 18/V/2014

Citation: T. K. Yuldashev, “A Double Inverse Problem for Fredholm Integro-Differential Equation of Elliptic Type”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(35) (2014), 39–49

Citation in format AMSBIB
\Bibitem{Yul14}
\by T.~K.~Yuldashev
\paper A Double Inverse Problem for Fredholm Integro-Differential Equation of Elliptic Type
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 2(35)
\pages 39--49
\mathnet{http://mi.mathnet.ru/vsgtu1306}
\crossref{https://doi.org/10.14498/vsgtu1306}
\zmath{https://zbmath.org/?q=an:06968874}


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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. Yuldashev T. K., “Upravlenie v nelineinoi obratnoi zadache dlya odnoi sistemy s differentsialnym uravneniem psevdoparabolicheskogo tipa”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Sistemnyi analiz i informatsionnye tekhnologii, 2015, no. 1, 23–31  elib
    2. T. K. Yuldashev, “Obratnaya zadacha dlya nelineinogo integro-differentsialnogo uravneniya Fredgolma chetvertogo poryadka s vyrozhdennym yadrom”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:4 (2015), 736–749  mathnet  crossref  zmath  elib
    3. T. K. Yuldashev, “Obyknovennoe integro-differentsialnoe uravnenie s vyrozhdennym yadrom i integralnym usloviem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:4 (2016), 644–655  mathnet  crossref  zmath  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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