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 J. Sib. Fed. Univ. Math. Phys., 2019, Volume 12, Issue 3, Pages 298–309 (Mi jsfu759)

On uniqueness and continuous dependence on the initial data of the solution of a system of two loaded parabolic equations with the Cauchy data

Igor V. Frolenkov, Irina S. Antipina, Natalya M. Terskikh

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

Abstract: We study the Cauchy problem for the system of one-dimensional loaded parabolic equations. Uniqueness and continuous dependence of solutions on the initial data in the class of smooth bounded functions is proved.

Keywords: loaded equation, system of parabolic equation, weak approximation method, Cauchy problem, uniqueness, continuous dependence of the solution on the initial data.

DOI: https://doi.org/10.17516/1997-1397-2019-12-3-298-309

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UDC: 517.9
Accepted: 03.02.2019
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Citation: Igor V. Frolenkov, Irina S. Antipina, Natalya M. Terskikh, “On uniqueness and continuous dependence on the initial data of the solution of a system of two loaded parabolic equations with the Cauchy data”, J. Sib. Fed. Univ. Math. Phys., 12:3 (2019), 298–309

Citation in format AMSBIB
\Bibitem{FroAntTer19} \by Igor~V.~Frolenkov, Irina~S.~Antipina, Natalya~M.~Terskikh \paper On uniqueness and continuous dependence on the initial data of the solution of a system of two loaded parabolic equations with the Cauchy data \jour J. Sib. Fed. Univ. Math. Phys. \yr 2019 \vol 12 \issue 3 \pages 298--309 \mathnet{http://mi.mathnet.ru/jsfu759} \crossref{https://doi.org/10.17516/1997-1397-2019-12-3-298-309} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000471028500004}