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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2024, Volume 9, Issue 4, Pages 585–595
DOI: https://doi.org/10.47475/2500-0101-2024-9-4-585-595
(Mi chfmj405)
 

Mathematics

Third-order differential equations with multiple characteristics: degeneration and unknown external influence

A. I. Kozhanovabc, G. R. Ashurovad

a S.L. Sobolev Institute of Mathematics, Novosibirsk, Russia
b Новосибирский государственный университет, Новосибирск, Россия
c Yugra State University, Khanty-Mansiysk, Russia
d Al-Farabi Kazakh National University, Almaty, Kazakhstan
References:
Abstract: Inverse problems of determination together with the solution of a degenerate differential equation with multiple characteristics of an unknown coefficient representing external influence (the free term) are studied. The nature of degeneration in the studied equation, as well as the type of the unknown coefficient, are determined by the time variable. Theorems of existence and uniqueness of regular solutions (solutions that possess all generalized derivatives according to S.L. Sobolev, which are involved in the equation) are proved for the studied problems.
Keywords: differential equation with multiple characteristics, degeneration, inverse problem, unknown external influence, regular solution, existence, uniqueness.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FENG-2023-0004
The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation, theme “Analytical and numerical study of inverse problems on recovering parameters of atmosphere or water sources and (or) parameters of media” (code FENG-2023-0004).
Received: 10.08.2024
Revised: 27.09.2024
Document Type: Article
UDC: 517.95
Language: Russian
Citation: A. I. Kozhanov, G. R. Ashurova, “Third-order differential equations with multiple characteristics: degeneration and unknown external influence”, Chelyab. Fiz.-Mat. Zh., 9:4 (2024), 585–595
Citation in format AMSBIB
\Bibitem{KozAsh24}
\by A.~I.~Kozhanov, G.~R.~Ashurova
\paper Third-order differential equations with multiple characteristics: degeneration and unknown external influence
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2024
\vol 9
\issue 4
\pages 585--595
\mathnet{http://mi.mathnet.ru/chfmj405}
\crossref{https://doi.org/10.47475/2500-0101-2024-9-4-585-595}
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