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Matematicheskie Zametki, 2025, Volume 117, Issue 6, Pages 928–942
DOI: https://doi.org/10.4213/mzm14597 (Mi mzm14597) 		 
Series expansions of solutions of differential-difference parabolic equations

A. B. Muravnika, O. E. Yaremkob, N. N. Yaremkoc

a Peoples' Friendship University of Russia named after Patrice Lumumba, Moscow
b Moscow State Technological University "Stankin"
c National University of Science and Technology «MISIS», Moscow
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DOI: https://doi.org/10.4213/mzm14597
Abstract: The Cauchy problem for parabolic differential-difference equations with operators that are sums of differential operators and translation operators and with operators that are their superpositions is investigated. Expansions of solutions of the indicated problem into function series are constructed. The domains of convergence (including uniform convergence) of the indicated series are established.
Keywords: differential-difference equation, parabolic equation, Cauchy problem, translation with respect to spatial variables, series expansion of solutions.
Funding agency Grant number
Russian Science Foundation 24-11-00073
Ministry of Science and Higher Education of the Russian Federation FSFS-2024-0007
The research of the first author described in Sec. 2 was supported by the grant of the Russian Science Foundation no. 24-11-00073, https://rscf.ru/en/project/24-11-00073/. The research of the second and third authors described in Sec. 3 was supported by the Ministry of Science and Education of the Russian Federation (grant no. FSFS-2024-0007).
Received: 18.12.2024
Published: 19.08.2025
English version:
Mathematical Notes, 2025, Volume 117, Issue 6, Pages 1051–1064
DOI: https://doi.org/10.1134/S0001434625602941
Bibliographic databases:
Document Type: Article
UDC: 517.956
PACS: 02.30.Jr
MSC: 47E07
Language: Russian
Citation: A. B. Muravnik, O. E. Yaremko, N. N. Yaremko, “Series expansions of solutions of differential-difference parabolic equations”, Mat. Zametki, 117:6 (2025), 928–942; Math. Notes, 117:6 (2025), 1051–1064
Citation in format AMSBIB
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\by A.~B.~Muravnik, O.~E.~Yaremko, N.~N.~Yaremko
\paper Series expansions of solutions of differential-difference parabolic equations
\jour Mat. Zametki
\yr 2025
\vol 117
\issue 6
\pages 928--942
\mathnet{http://mi.mathnet.ru/mzm14597}
\crossref{https://doi.org/10.4213/mzm14597}
\transl
\jour Math. Notes
\yr 2025
\vol 117
\issue 6
\pages 1051--1064
\crossref{https://doi.org/10.1134/S0001434625602941}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105015200389}
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