Kh. G. Umarov, “Blow-up of a solution and global solvability of the Cauchy problem for the equation modeling the propagation of longitudinal strain waves”, Sibirsk. Mat. Zh., 2025, Volume 66, Number 2,Pages <nobr>316

Blow-up of a solution and global solvability of the Cauchy problem for the equation modeling the propagation of longitudinal strain waves

Kh. G. Umarov^ab

^a Academy of Sciences of the Chechen Republic, Grozny, Russia
^b Chechen State Pedagogical University, Grozny, Russia

Abstract: For a nonlinear dispersion-dissipation Sobolev-type partial differential equation modeling the propagation of longitudinal strain waves in a nonlinear elastic rod, the Cauchy problem is studied in the space of continuous functions defined on the entire real axis and having limits at infinity. Some conditions ensuring existence of a global solution and blow-up of a solution to the Cauchy problem on a finite time interval are exposed.

Keywords: longitudinal strain waves in a nonlinear elastic rod, nonlinear Sobolev-type equation, global solution, blow-up of a solution.

UDC: 517.958

MSC: 35R30

Received: 07.01.2024
Revised: 26.01.2025
Accepted: 25.02.2025

DOI: 10.33048/smzh.2025.66.213