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Matematicheskie Zametki, 2023, Volume 113, Issue 5, Pages 747–763
DOI: https://doi.org/10.4213/mzm13781 (Mi mzm13781) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the Solvability of Nonlinear Parabolic Functional-Differential Equations with Shifts in the Spatial Variables

O. V. Solonukhaab

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
b Peoples' Friendship University of Russia, Moscow
Full-text PDF (728 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm13781
Abstract: The first mixed boundary value problem for a nonlinear functional-differential equation of parabolic type with shifts in the spatial variables is considered. Sufficient conditions are proved under which a nonlinear differential-difference operator is demicontinuous, coercive, and pseudomonotone on the domain of the operator $\partial_t$. Based on these properties, existence theorems for a generalized solution are proved.
Keywords: nonlinear parabolic functional-differential equation, shift operator, pseudomonotone operator on $W$, ellipticity condition.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-1115
This work was supported by the Ministry for Science and Higher Education of the Russian Federation (megagrant no. 075-15-2022-1115).
Received: 20.10.2022
Revised: 07.12.2022
English version:
Mathematical Notes, 2023, Volume 113, Issue 5, Pages 708–722
DOI: https://doi.org/10.1134/S0001434623050115
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 34K99, 35K61, 35K20
Language: Russian
Citation: O. V. Solonukha, “On the Solvability of Nonlinear Parabolic Functional-Differential Equations with Shifts in the Spatial Variables”, Mat. Zametki, 113:5 (2023), 747–763; Math. Notes, 113:5 (2023), 708–722
Citation in format AMSBIB
\Bibitem{Sol23}
\by O.~V.~Solonukha
\paper On the Solvability of Nonlinear Parabolic Functional-Differential
Equations with Shifts in the Spatial Variables
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 5
\pages 747--763
\mathnet{http://mi.mathnet.ru/mzm13781}
\crossref{https://doi.org/10.4213/mzm13781}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4602433}
\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 5
\pages 708--722
\crossref{https://doi.org/10.1134/S0001434623050115}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85163189990}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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