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arXiv · 1010.5689

The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

H. A. Erbay·A. Erkip·G. M. Muslu
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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.

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H. A. Erbay, A. Erkip, G. M. Muslu. 2010-10-27. The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model. https://doi.org/10.1016/j.jde.2012.01.008

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