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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 9, Pages 59–67 (Mi ivm9152)  

This article is cited in 5 scientific papers (total in 5 papers)

Inverse problem for a nonlinear Benney–Luke type integro-differential equations with degenerate kernel

T. K. Yuldashev

Siberian State Aerospace University, 31 Krasnoyarskii Rabochii Ave., Krasnoyarsk, 660014 Russia

Abstract: We consider the questions of unique solvability of the inverse problem for a nonlinear partial Benney–Luke type integro-differential equation of the fourth order with degenerate kernel. The method of degenerate kernel designed for Fredholm integral equations of the second kind is modified to the case of considered partial Benney–Luke type integro-differential equation of the fourth order. We use the Fourier method of separation of variables. After designation, the Benney–Luke type integro-differential equation is reduced to a system of algebraic equations. With the help of additional condition we obtain the countable system of nonlinear integral equations with respect to main unknown function. We use the method of successive approximations combined with the method of compressing maps. Further is defined the restore function.

Keywords: inverse problem, integro-differential equation, Benney–Luke type equation, degenerate kernel, system of algebraic equations, unique solvability.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:9, 53–60

Bibliographic databases:

UDC: 517.95
Received: 05.02.2015

Citation: T. K. Yuldashev, “Inverse problem for a nonlinear Benney–Luke type integro-differential equations with degenerate kernel”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 9, 59–67; Russian Math. (Iz. VUZ), 60:9 (2016), 53–60

Citation in format AMSBIB
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\by T.~K.~Yuldashev
\paper Inverse problem for a~nonlinear Benney--Luke type integro-differential equations with degenerate kernel
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 9
\pages 59--67
\mathnet{http://mi.mathnet.ru/ivm9152}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 9
\pages 53--60
\crossref{https://doi.org/10.3103/S1066369X16090061}
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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, “Obratnaya zadacha dlya obyknovennogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom i nelokalnymi integralnymi usloviyami”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2016, no. 3, 19–33  mathnet  crossref  elib
    2. T. K. Yuldashev, “Ob odnoi nelokalnoi zadache dlya neodnorodnogo integro-differentsialnogo uravneniya tipa Bussineska s vyrozhdennym yadrom”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 159, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2017, 88–99  mathnet  mathscinet  elib
    3. T. K. Yuldashev, “Determination of the coefficient and boundary regime in boundary value problem for integro-differential equation with degenerate kernel”, Lobachevskii J. Math., 38:3, SI (2017), 547–553  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. T. K. Yuldashev, “Nonlocal boundary value problem for a nonlinear Fredholm integro-differential equation with degenerate kernel”, Differ. Equ., 54:12 (2018), 1646–1653  crossref  mathscinet  zmath  isi  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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