BLOW-UP OF THE SOLUTION AND GLOBAL SOLVABILITY OF THE CAUCHY PROBLEM FOR THE EQUATION OF VIBRATIONS OF A HOLLOW ROD

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.

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Publication Details

Journal
Дифференциальные уравнения / Differential Equations
Published
2025-01-01
DOI
https://doi.org/10.7868/s3034503025010062
Primary Topic
Vibration and Dynamic Analysis
Type
article
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article

BLOW-UP OF THE SOLUTION AND GLOBAL SOLVABILITY OF THE CAUCHY PROBLEM FOR THE EQUATION OF VIBRATIONS OF A HOLLOW ROD

Х. Г. Умаров
Дифференциальные уравнения / Differential Equations
Vibration and Dynamic Analysis
article

BLOW-UP OF THE SOLUTION AND GLOBAL SOLVABILITY OF THE CAUCHY PROBLEM FOR THE EQUATION OF VIBRATIONS OF A HOLLOW ROD

Х. Г. Умаров
article en

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.

Дифференциальные уравнения / Differential EquationsVol. 61(1)
Openalex Percentile: Top 66%
Vibration and Dynamic Analysis
DOISourceOpenAlex
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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 — Х. Г. Умаров · Дифференциальные уравнения / Differential Equations (2025) | TGRS Research Map | TGRS