Abstract
For a nonlinear differential equation of Sobolev type describing the longitudinal vibrations of a thick rod with allowance for its transverse inertia, we study the solvability of the Cauchy problem in the half-plane \((x,t)\in \mathbb {R}^1\times [0,+\infty ) \) in the class of functions that, for each fixed value of the time variable \( t\geq 0\), are continuous on the entire real line and have finite limits at infinity. Both sufficient conditions for the existence of a global solution of the Cauchy problem and sufficient conditions for its blowup on a finite time interval are found.
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Translated by V. Potapchouck
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Umarov, K.G. Cauchy Problem for the Equation of Longitudinal Vibrations of a Thick Rod with Allowance for Transverse Inertia. Diff Equat 58, 65–80 (2022). https://doi.org/10.1134/S0012266122010086
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DOI: https://doi.org/10.1134/S0012266122010086