English

The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

Analysis of PDEs 2020-08-04 v2

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.

Keywords

Cite

@article{arxiv.1010.5689,
  title  = {The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model},
  author = {H. A. Erbay and A. Erkip and G. M. Muslu},
  journal= {arXiv preprint arXiv:1010.5689},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-21T16:34:56.714Z