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BLOW-UP OF THE SOLUTION AND GLOBAL SOLVABILITY OF THE CAUCHY PROBLEM FOR THE EQUATION OF VIBRATIONS OF A HOLLOW ROD
- Authors: Umarov K.G.1,2
-
Affiliations:
- Academy of Sciences of the Chechen Republic
- Chechen State Pedagogical University
- Issue: Vol 61, No 1 (2025)
- Pages: 68-83
- Section: PARTIAL DERIVATIVE EQUATIONS
- URL: https://journal-vniispk.ru/0374-0641/article/view/291485
- DOI: https://doi.org/10.31857/S0374064125010062
- EDN: https://elibrary.ru/HZTIEE
- ID: 291485
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Abstract
For a nonlinear partial differential equation of Sobolev type, generalizing the equation of oscillations of a hollow flexible rod, the Cauchy problem is studied in the space of continuous functions defined on the entire numerical axis and for which there are limits at infinity. The conditions for the existence of a global classical solution and the blow-up of the solution to the Cauchy problem on a finite time interval are considered.
About the authors
Kh. G. Umarov
Academy of Sciences of the Chechen Republic; Chechen State Pedagogical University
Email: umarov50@mail.ru
Grozny, Russia; Grozny, Russia
References
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