Solution Blow-Up and Global Solvability of the Cauchy Problem for a Model Third-Order Partial Differential Equation

We obtain conditions for the existence of a global solution and the blow-up of the solution of the Cauchy problem on a finite time interval for a nonlinear third-order partial differential equation generalizing the equation of torsion vibrations of a cylindrical rod with allowance for internal and e...

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Bibliographic Details
Published in:Differential equations 2023, Vol.59 (1), p.51-73
Main Author: Umarov, Kh. G.
Format: Article
Language:English
Subjects:
Cauchy problems
Damping
Difference and Functional Equations
Differential equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Stress propagation
Stress waves
Wave propagation
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Summary:We obtain conditions for the existence of a global solution and the blow-up of the solution of the Cauchy problem on a finite time interval for a nonlinear third-order partial differential equation generalizing the equation of torsion vibrations of a cylindrical rod with allowance for internal and external damping modeling the propagation of longitudinal stress waves along a one-dimensional viscoelastic rod whose the material obeys Voigt–Kelvin medium deformation law.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266123010056