The Cauchy problem for a one dimensional nonlinear elastic peridynamic model

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