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.
Original language | English |
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Pages (from-to) | 4392-4409 |
Number of pages | 18 |
Journal | Journal of Differential Equations |
Volume | 252 |
Issue number | 8 |
DOIs | |
Publication status | Published - 15 Apr 2012 |
Keywords
- Blow-up
- Global existence
- Nonlinear peridynamic equation
- Nonlocal Cauchy problem