 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 54, Issue 5 / 2019 | Next article >> |
| Kh.G. Umarov, "Cauchy Problem for the Torsional Vibration Equation of a Nonlinear-Elastic Rod of Infinite Length," Mech. Solids. 54 (5), 726-740 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
5 |
Pages |
726-740 |
| DOI |
10.3103/S0025654419050194 |
| Title |
Cauchy Problem for the Torsional Vibration Equation of a Nonlinear-Elastic Rod of Infinite Length |
| Author(s) |
Kh.G. Umarov (Academy of Sciences of the Chechen Republic, Groznyi, 364024 Russia, umarov50@mail.ru) |
| Abstract |
For the differential equation of torsional vibrations of an infinite nonlinear-elastic rod, the
solvability of the Cauchy problem in the space of continuous functions on the real axis is studied.
An explicit form of the solution of the corresponding linear partial differential equation is obtained.
The time interval for the existence of the classical solution to the Cauchy problem for a nonlinear
equation is found and an estimate of this local solution is obtained. Conditions for the existence of a
global solution and blow-up of the solution on a finite interval are considered. |
| Keywords |
torsional vibrations, Sobolev-type nonlinear equations, global solvability, solution blow-up |
| Received |
14 June 2018 | Revised |
06 December 2018 | Accepted |
25 December 2018 |
| Link to Fulltext |
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