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Sibirskii Zhurnal Industrial'noi Matematiki, 2024, Volume 27, Number 2, Pages 112–120
DOI: https://doi.org/10.33048/SIBJIM.2024.27.208
(Mi sjim1284)
 

On some linear two-dimensional Volterra integral equations of the first kind

S. V. Solodusha

Melentiev Energy Systems Institute of the Siberian Branch of the Russian Academy of Sciences, Irkutsk, 664033 Russia
References:
Abstract: The problem of identifying Volterra kernels is an important stage in the construction of integral models of nonlinear dynamical systems based on the tool of Volterra series. The paper considers a new class of two-dimensional integral equations that arise when recovering nonsymmetric kernels in a Volterra polynomial of the second degree, where $x(t)$ is the input vector function of time. The strategy for choosing test signals used to solve this problem is based on applying piecewise linear functions (with a rising edge). An explicit inversion formula is constructed for the selected type of Volterra equations of the first kind with variable integration limits. The questions of existence and uniqueness of solutions of the corresponding equations in the class $C_{[0,T]}$ are studied.
Keywords: two-dimensional Volterra integral equation of the first kind, identification, inversion formula.
Funding agency Grant number
Russian Science Foundation 22-21-00409
Received: 20.11.2023
Revised: 07.03.2024
Accepted: 22.05.2024
English version:
Journal of Applied and Industrial Mathematics, 2024, Volume 18, Issue 2, Pages 344–351
DOI: https://doi.org/10.1134/S1990478924020157
Document Type: Article
UDC: 519.642
Language: Russian
Citation: S. V. Solodusha, “On some linear two-dimensional Volterra integral equations of the first kind”, Sib. Zh. Ind. Mat., 27:2 (2024), 112–120; J. Appl. Industr. Math., 18:2 (2024), 344–351
Citation in format AMSBIB
\Bibitem{Sol24}
\by S.~V.~Solodusha
\paper On some linear two-dimensional Volterra integral equations of the first kind
\jour Sib. Zh. Ind. Mat.
\yr 2024
\vol 27
\issue 2
\pages 112--120
\mathnet{http://mi.mathnet.ru/sjim1284}
\crossref{https://doi.org/10.33048/SIBJIM.2024.27.208}
\transl
\jour J. Appl. Industr. Math.
\yr 2024
\vol 18
\issue 2
\pages 344--351
\crossref{https://doi.org/10.1134/S1990478924020157}
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    Сибирский журнал индустриальной математики
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