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.
Key words:longitudinal waves in a viscoelastic rod, nonlinear Sobolev-type equations, global solution, solution blow-up.
