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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 149, Pages 129–140 (Mi into326)  
This article is cited in 16 scientific papers (total in 16 papers)

Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-type Equation with Degenerate Kernel

T. K. Yuldashev

M. F. Reshetnev Siberian State University of Science and Technologies
Full-text PDF (202 kB) Citations (16)
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Abstract: We discuss questions on the unique solvability of inverse boundary-value source problems for a certain nonlinear integro-differential equation of Boussinesq type with degenerate kernel. We develop the method of degenerate kernels for the inverse boundary-value problem for a fourth-order integro-differential partial differential equation. Using the Banach fixed-point theorem, we prove the uniquely solvability of the problem and establish a criterion of stability of solutions with respect to recovery functions.
Keywords: inverse boundary-value problem, integro-differential Boussinesq-type equation, degenerate kernel, unique solvability.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 250, Issue 5, Pages 847–858
DOI: https://doi.org/10.1007/s10958-020-05050-2
Bibliographic databases:
Document Type: Article
UDC: 517.968
MSC: 35R30
Language: Russian
Citation: T. K. Yuldashev, “Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-type Equation with Degenerate Kernel”, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 149, VINITI, Moscow, 2018, 129–140; J. Math. Sci. (N. Y.), 250:5 (2020), 847–858
Citation in format AMSBIB
\Bibitem{Yul18}
\by T.~K.~Yuldashev
\paper Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-type Equation with Degenerate Kernel
\inbook Proceedings of the International Conference ``Actual Problems of Applied Mathematics and Physics,'' Kabardino-Balkaria, Nalchik, May 17--21, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 149
\pages 129--140
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into326}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847732}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 250
\issue 5
\pages 847--858
\crossref{https://doi.org/10.1007/s10958-020-05050-2}
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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