This article is cited in 8 papers

Blow-up and global solvability of the Cauchy problem for a pseudohyperbolic equation related to the generalized Boussinesq equation

Kh. G. Umarov<sup>ab

a</sup> Academy of Sciences of Chechen Republic
^b Chechen State University, Groznyi

Abstract: Under consideration is the Cauchy problem in the space of continuous functions for a nonlinear strictly hyperbolic equation related to the generalized Boussinesq equation. We discuss the conditions for existence of a global classical solution and blow-up of a solution to the Cauchy problem on a finite time segment.

Keywords: sixth order generalized Boussinesq equation, nonlinear strictly pseudohyperbolic equation, global solution, blow-up.

UDC: 517.958

MSC: 35R30

Received: 27.07.2021
Revised: 03.02.2022
Accepted: 10.02.2022

DOI: 10.33048/smzh.2022.63.315

 English version: Siberian Mathematical Journal, 2022, 63:3, 559–574