Solution Blow-Up and Global Solvability of the Cauchy Problem for the Equation of Moderately Long Longitudinal Waves in a Viscoelastic Rod

Abstract

The Cauchy problem for a nonlinear Sobolev-type differential equation modeling moderately long small-amplitude longitudinal waves in a viscoelastic rod is investigated in a space of continuous functions defined on the entire number line that have limits at infinity. Conditions for the existence of a global solution and for finite time solution blow-up are examined.