The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

Abstract

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.To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages)