The Cauchy problem for a one-dimensional nonlinear elastic peridynamic model

Erbay H. A., Erkip A., Muslu G. M.

JOURNAL OF DIFFERENTIAL EQUATIONS, vol.252, no.8, pp.4392-4409, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 252 Issue: 8
  • Publication Date: 2012
  • Doi Number: 10.1016/j.jde.2012.01.008
  • Journal Name: JOURNAL OF DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4392-4409
  • Istanbul Technical University Affiliated: Yes

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. (C) 2012 Elsevier Inc. All rights reserved.