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 J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 3, Pages 364–373 (Mi jsfu495)

On the solvability of a system of two multidimensional loaded parabolic equations with the Cauchy data

Galina V. Romanenko, Igor V. Frolenkov

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: We study a multidimensional system of two loaded parabolic equations of a special kind with the Cauchy data. Sufficient conditions for the existence of a solution in the class of smooth bounded functions are obtained. The splitting method at differential level (the method of weak approximation) is used in the proof.

Keywords: inverse problem, direct problem, loaded equation, parabolic equation, weak approximation method, system of partial differential equations, Cauchy problem.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 14.Y26.31.0006 The research for this paper was carried out in Siberian Federal University within the framework of the project "Multidimensional Complex Analysis and Differential Equations" funded by the grant of the Russian Federation Government to support scientific research under supervision of a leading scientist, no. 14.Y26.31.0006.

DOI: https://doi.org/10.17516/1997-1397-2016-9-3-364-373

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UDC: 517.9
Received in revised form: 03.04.2016
Accepted: 15.06.2016
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Citation: Galina V. Romanenko, Igor V. Frolenkov, “On the solvability of a system of two multidimensional loaded parabolic equations with the Cauchy data”, J. Sib. Fed. Univ. Math. Phys., 9:3 (2016), 364–373

Citation in format AMSBIB
\Bibitem{RomFro16} \by Galina~V.~Romanenko, Igor~V.~Frolenkov \paper On the solvability of a system of two multidimensional loaded parabolic equations with the Cauchy data \jour J. Sib. Fed. Univ. Math. Phys. \yr 2016 \vol 9 \issue 3 \pages 364--373 \mathnet{http://mi.mathnet.ru/jsfu495} \crossref{https://doi.org/10.17516/1997-1397-2016-9-3-364-373} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000412010000012} 

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This publication is cited in the following articles:
1. I. V. Frolenkov, E. N. Kriger, “O razreshimosti zadachi Koshi dlya odnogo klassa mnogomernykh nagruzhennykh parabolicheskikh uravnenii”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 41–57
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