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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 2, Pages 76–85 (Mi vmj583)  

This article is cited in 2 scientific papers (total in 2 papers)

Inverse problem for a third order Fredholm integro-differential equation with degenerate kernel

T. K. Yuldashev

M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, Russia

Abstract: It is considered the questions of one value solvability of the inverse problem for a third order nonlinear partial Fredholm type integro-differential equation with degenerate kernel. The method of degenerate kernel for second kind Fredholm integral equations is modified for the case of third order partial Fredholm type integro-differential equation. The Fredholm type integro-differential equation is reduced to a system of algebraic equations. By the aid of additional condition it is obtained a second kind nonlinear Volterra type integral equation with respect to main unknown function and a first kind linear Volterra type integral equation with respect to restore function. It is used the method of compressing maps, which gave us the real method of finding the solutions – the method of successive approximations. Further is defined the restore function.

Key words: inverse problem, integro-differential equation, Fredholm type equation, degenerate kernel, system of algebraic equations, one valued solvability.

Full text: PDF file (190 kB)
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UDC: 517.95
Received: 19.05.2015

Citation: T. K. Yuldashev, “Inverse problem for a third order Fredholm integro-differential equation with degenerate kernel”, Vladikavkaz. Mat. Zh., 18:2 (2016), 76–85

Citation in format AMSBIB
\Bibitem{Yul16}
\by T.~K.~Yuldashev
\paper Inverse problem for a~third order Fredholm integro-differential equation with degenerate kernel
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 2
\pages 76--85
\mathnet{http://mi.mathnet.ru/vmj583}


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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. 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
    2. T. K. Yuldashev, “Ob odnoi nelokalnoi obratnoi zadache dlya nelineinogo integro-differentsialnogo uravneniya Benney-Luke s vyrozhdennym yadrom”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2018, no. 3, 19–41  mathnet  crossref  elib
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