  This paper studies the Cauchy problem for a one-dimensional nonlinear
peridynamic model describing the dynamic response of an infinitely long elastic
bar. The issues of local well-posedness and smoothness of the solutions are
discussed. The existence of a global solution is proved first in the sublinear
case and then for nonlinearities of degree at most three. The conditions for
finite-time blow-up of solutions are established.
