Erbay, Hüsnü AtaErkip, A.Muslu, G. M.2012-08-032012-08-032012-04-150022-0396http://hdl.handle.net/10679/226https://doi.org/10.1016/j.jde.2012.01.008This 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.enginfo:eu-repo/semantics/openAccessArticle25284392440900030086130000310.1016/j.jde.2012.01.008Nonlocal cauchy problemNonlinear peridynamic equationGlobal existenceBlow-up2-s2.0-84856769497