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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 1, Pages 198–209
DOI: https://doi.org/10.33048/smzh.2021.62.117 (Mi smj7549) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The Cauchy problem for the nonlinear long longitudinal waves equation in a viscoelastic rod

Kh. G. Umarovab

a Academy of Sciences of the Chechen Republic, Grozny, Russia
b Chechen State Pedagogical University, Grozny, Russia
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DOI: https://doi.org/10.33048/smzh.2021.62.117
Abstract: We study the Cauchy problem in the space of continuous functions for some nonlinear differential equation of Sobolev type that simulates longitudinal waves in an infinite viscoelastic rod. Under consideration are the conditions for the existence of the global classical solution and the blow-up of the solution to the Cauchy problem on a finite time interval.
Keywords: longitudinal waves in a viscoelastic rod, Sobolev-type equations, global solution, blow-up of the solution.
Received: 09.04.2020
Revised: 09.04.2020
Accepted: 09.10.2020
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 1, Pages 159–168
DOI: https://doi.org/10.1134/S0037446621010171
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 35R30
Language: Russian
Citation: Kh. G. Umarov, “The Cauchy problem for the nonlinear long longitudinal waves equation in a viscoelastic rod”, Sibirsk. Mat. Zh., 62:1 (2021), 198–209; Siberian Math. J., 62:1 (2021), 159–168
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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