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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 7, Pages 1177–1191
DOI: https://doi.org/10.31857/S0044466923070177 (Mi zvmmf11588) 		 
Partial Differential Equations

Solution blow-up and global solvability of the Cauchy problem for the equation of moderately long longitudinal waves in a viscoelastic rod

Kh. G. Umarovab

a Academy of Sciences of the Chechen Republic, 364061, Grozny, Russia
b Chechen State Pedagogical University, 364068, Grozny, Russia
DOI: https://doi.org/10.31857/S0044466923070177
Abstract: The Cauchy problem for a nonlinear Sobolev-type differential equation modeling moderately long small-amplitude longitudinal waves in a viscoelastic rod is investigated in a space of continuous functions defined on the entire number line that have limits at infinity. Conditions for the existence of a global solution and for finite time solution blow-up are examined.
Key words: longitudinal waves in a viscoelastic rod, nonlinear Sobolev-type equations, global solution, solution blow-up.
Received: 21.12.2022
Revised: 21.12.2022
Accepted: 30.03.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 7, Pages 1285–1299
DOI: https://doi.org/10.1134/S0965542523070151
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: Kh. G. Umarov, “Solution blow-up and global solvability of the Cauchy problem for the equation of moderately long longitudinal waves in a viscoelastic rod”, Zh. Vychisl. Mat. Mat. Fiz., 63:7 (2023), 1177–1191; Comput. Math. Math. Phys., 63:7 (2023), 1285–1299
Citation in format AMSBIB
\Bibitem{Uma23}
\by Kh.~G.~Umarov
\paper Solution blow-up and global solvability of the Cauchy problem for the equation of moderately long longitudinal waves in a viscoelastic rod
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 7
\pages 1177--1191
\mathnet{http://mi.mathnet.ru/zvmmf11588}
\crossref{https://doi.org/10.31857/S0044466923070177}
\elib{https://elibrary.ru/item.asp?id=54238538}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 7
\pages 1285--1299
\crossref{https://doi.org/10.1134/S0965542523070151}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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