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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 11, Pages 1850–1858
DOI: https://doi.org/10.31857/S0044466923110042 (Mi zvmmf11650) 		 
Partial Differential Equations

Exact solutions of a nonlinear equation describing blow-up instability in self-oscillatory systems

A. I. Aristovab

a Faculty of Computational Mathematics and Cybernetics, Moscow State University, 119992, Moscow, Russia
b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 119333, Moscow, Russia
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DOI: https://doi.org/10.31857/S0044466923110042
Abstract: A nonclassical fourth-order partial differential equation describing blow-up instability in self-oscillatory systems is studied. Several classes of exact solutions of this equation are constructed. It is shown that these solutions include ones growing to infinity in a finite time, ones bounded globally in time, and ones bounded on any finite time interval, but not globally.
Key words: nonlinear partial differential equations, blow-up of solutions, exact solutions.
Funding agency Grant number
Russian Science Foundation 22-21-00449
This work was supported in part by the Russian Science Foundation, project no. 22-21-00449.
Received: 13.03.2023
Revised: 28.03.2023
Accepted: 30.04.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 11, Pages 2081–2089
DOI: https://doi.org/10.1134/S0965542523110027
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. I. Aristov, “Exact solutions of a nonlinear equation describing blow-up instability in self-oscillatory systems”, Zh. Vychisl. Mat. Mat. Fiz., 63:11 (2023), 1850–1858; Comput. Math. Math. Phys., 63:11 (2023), 2081–2089
Citation in format AMSBIB
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\by A.~I.~Aristov
\paper Exact solutions of a nonlinear equation describing blow-up instability in self-oscillatory systems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 11
\pages 1850--1858
\mathnet{http://mi.mathnet.ru/zvmmf11650}
\crossref{https://doi.org/10.31857/S0044466923110042}
\elib{https://elibrary.ru/item.asp?id=54720593}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 11
\pages 2081--2089
\crossref{https://doi.org/10.1134/S0965542523110027}
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