Abstract:
Propagation of nonlinear longitudinal elastic waves in a metamaterial (gradient-elastic medium) is modeled using a nonlinear Sobolev-type differential equation, for which the Cauchy problem in the space of continuous functions is investigated. Conditions for the existence of a global solution and for solution blow-up on a finite time interval are considered.
Key words:one-dimensional equation of motion in gradient-elastic medium, nonlinear Sobolev-type equation, global solution, solution blow-up.
