Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 208, Pages 3–10
DOI: https://doi.org/10.36535/0233-6723-2022-208-3-10 (Mi into988) 		 
On two-dimensional systems of Volterra integral equations of the first kind

M. V. Bulatov, L. S. Solovarova

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk
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DOI: https://doi.org/10.36535/0233-6723-2022-208-3-10
Abstract: In this paper, we consider two-dimensional systems of Volterra integral equations of the first kind. The case where a system of integral equations of the second kind is obtained by differentiating the equations is well studied. We examine the case where this approach leads to a system of integral equations with an degenerate matrix of the principal part. We formulate sufficient conditions for the existence of a unique smooth solution in terms of matrix pencils.
Keywords: two-dimensional integral equation of Volterra type, integro-algebraic equation, matrix pencil.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-S52003
20-51-54003
This work was supported by the Russian Foundation for Basic Research (project Nos. 20-51-S52003, 20-51-54003).
Document Type: Article
UDC: 517.968.2
MSC: 35R09, 45Fxx, 45Dxx
Language: Russian
Citation: M. V. Bulatov, L. S. Solovarova, “On two-dimensional systems of Volterra integral equations of the first kind”, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 208, VINITI, Moscow, 2022, 3–10
Citation in format AMSBIB
\Bibitem{BulSol22}
\by M.~V.~Bulatov, L.~S.~Solovarova
\paper On two-dimensional systems of Volterra integral equations of the first kind
\inbook Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 208
\pages 3--10
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into988}
\crossref{https://doi.org/10.36535/0233-6723-2022-208-3-10}
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