Partial Differential Equations

Blow-up of the solution to the equation for nonlinear beam vibrations with allowance for transverse deformation effects

Kh. G. Umarov<sup>ab

a</sup> Academy of Sciences of the Chechen Republic, 364043, Grozny, Chechen Republic, Russia
^b Chechen State Pedagogical University, 364068, Grozny, Chechen Republic, Russia

Abstract: Beam vibrations with allowance for deformation effects in the transverse direction are modeled using a nonlinear Sobolev-type differential equation, for which the Cauchy problem is investigated in the space of continuous functions. Conditions for solution blow-up on a finite time interval are considered.

Key words: beam vibrations, nonlinear Sobolev-type equations, solution blow-up.

UDC: 517.958

Received: 14.05.2023
Revised: 14.05.2023
Accepted: 25.07.2023

DOI: 10.31857/S0044466923110273

 English version: Computational Mathematics and Mathematical Physics, 2023, 63:11, 2107–2122

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